Will edit this later with a response.
Edit:
This question is vague so my answer is going to be really long and it will feature a lot of general fighting game theory. More specific questions are easier to answer but I also feel like writing down my thoughts on the Marth matchup so this is as good a time as any.
I'll get this out of the way first: don't throw eggs against Marth unless you are on the ledge (and don't go to the ledge just to throw eggs). He will swat them for free or block and wavedash out. Any fast character will be able to get through onstage eggs without any trouble. They are unsafe and barely give you any reward except at very high %.
Marth wants to keep you at tipper range or just a little farther, where his moves beat yours and he is free to dash back out of the way of anything you can throw at him in situations where he doesn't have time to attack. This is also a range where he can read your retreat and catch you with Dtilt. Where you want to be is up to you, but generally Marth isn't comfortable when you get too close for him to tipper you or outspace your crouch cancel. Getting into this range requires you to corner him and get through his amazing hitboxes.
Any time Marth uses an approaching aerial, you should crouch cancel and down tilt it for a free techchase or the whole stage. Down Smash and Forward Tilt are also good options after the crouch cancel. Good Marths don't rely on approaching aerials against a grounded opponent. At the very least they'll do them in place so they don't slide forward after landing.
So what do you do against a well-spaced aerial instead?
Your options are:
1. Hit before the move is active (called a counter-hit)
2. Out-prioritize while the move is active
3. Hit after the move is active (called a whiff punish)
Retreating aerials are hard to whiff punish, and getting counterhits is hard in neutral because both players have a lot of control over their movement. And of course, Marth's aerials have extremely good priority. But your parry does beat them! It is also worth noting that the earlier a move is done, the easier it is to whiff punish and the harder it is to counter-hit, and vice-versa for late attacks. Retreating aerials also never hit unless you run into them, and they require the Marth to give up space.
So if Marth is using a retreating aerial, or even an aerial in place, he's doing it to stop you from coming at him. What's important to think about here is the idea that attacks aren't meant to hit your opponent, but instead control their movement. By doing that aerial, Marth is telling you that it's not safe to come into his space. If you run into it, he gets to follow-up, and if not, he is relatively safe. At least a lot safer than jumping towards you with that aerial!
If he does whiff the aerial, he's going to have a frame disadvantage, and you can use that to get a whiff punish or just back him into the corner. By placing yourself just outside the range of where your opponent is going to attack, you can take full advantage of his lag, and depending on how much of a frame advantage you have, either get a free hit, get a mix up by reading his next option, or let him take a safe way out of the situation and simply take space.
In most cases, a character can't do two aerials in one short hop. Generally they'll try to land while the hitbox is still out, so you get an advantage of however much landing lag they have (it tends to be 7-10 frames for most safe aerials). With this kind of small frame advantage, you have to be ready for the whiff punish way ahead of time if you want to get something guaranteed. Most of the time, especially in neutral, you're not that ready, and you have to react a bit later to the whiff and go for something that is not guaranteed. In this situation, you still have the advantage because none of Marth's options will start until his lag is over. That means if he just whiffed a Forward Air, and wants to Forward Air again, it's going to take him an extra 7 frames at the very least.
What this means is that even though Marth is only in a little lag, and something like your Down Tilt won't be a true whiff punish, if he tries to stop you from coming in, he'll lose this time. His Down Tilt might be able to stop yours when you're both actionable, but if he's just landed after a Forward Air, your Down Tilt will now hit before his! Now every character has a frame one option that protects them from attacks, and it tends to be helpful in this situation. If Marth blocks after landing, he won't get hit by your Down Tilt because it wasn't a "true whiff punish" (meaning it didn't hit during the actual endlag of the whiffed attack). This is where grabs come in (for everyone, not just Yoshi). If the threat of your Down Tilt beating his will make him block, he is going to block and wait for an attack. So instead you can come in with a grab. But be careful - your opponent will only block if they are afraid of getting hit.
If Marth doesn't want to play this guessing game where he has a disadvantage, he can try to back out of the situation by retreating. This usually means a dash back or wavedash back, but some characters and players like to jump away instead. If you read this, you can catch it by overshooting your approach and catching the movement back, or you can let the player retreat and eventually they will corner themselves and no longer be able to rely on that. Good tools for catching a retreat are run cancel Down Tilt and approaching Forward Air.
Marth's Short Hop Double Forward Air is a special case because it lets him do two aerials in one short hop, but your options for whiff punishing are mostly the same. You have about 30 frames in between the two Forward Airs, which is plenty of time to get a Back Air to hit if you are ready, and his second Forward Air can be punished on landing just like anything else. He does have mixups like double jump Forward Air or waveland so you will have to watch out for those.
Getting really solid whiff punishes on safe moves requires you to be pretty aware of what your opponent is going to do ahead of time, and you can't always know that (especially at the beginning of a match). In addition, it requires you to place yourself just outside the hitbox that you're trying to punish, so that leaves you at risk of being caught by something spaced closer to you. Because of this, you should also be able to challenge Marth's hitboxes directly. Yoshi does this by parrying.
The secret to getting really consistent parrying is to know when to use it, and to know how to influence your opponent's attack timings. If you're just fishing for a parry and you don't make an effort to use it along with your other tools, then your best bet is just to hope that Marth does something really obvious and also messes up his spacing so you can follow-up after the parry. This makes it too hard to parry, and you will get shut down by anyone who can vary their attack timings well (which is any decent player, whether or not they know the Yoshi matchup). Instead, if you want to parry, you have to give your opponent a reason to attack at a certain time.
If you're standing or crouching, waiting to parry, then Marth can easily stay outside the range of your attacks and he won't have to worry about them. You're also not moving, so he doesn't have to worry about his moves whiffing either. And most importantly, if at any point he doesn't like the situation, he can back off for free.
Instead, take the initiative to approach, and use your parry in conjunction with your approach options. Moving towards Marth, or towards some space that he is trying to control, will allow you to be more ambiguous. If you dash towards Marth, you could run cancel Down Tilt, Dash Attack, Dash Grab, Pivot Bair Air, or just dash back. But you also have the option of parrying, and because you're moving towards Marth, he can't ignore your attacks or your ability to continue dash dancing.
Your parry is for beating his attacks, and his attacks are for controlling space, so if he wants to defend his space, he's going to have to put out a hitbox or move out of the way and hope you whiff a move. But it is much more risky for him to vary his attack timings when a late attack will lose to your own attacks. If he's going to try a stationary Down Tilt to stop your grounded approach, he can't delay the Down Tilt or else he might get counter-hit by your Down Tilt, Dash Grab or Dash Attack. And if he feels like he can't delay his Down Tilt, then timing your parry is only a matter of knowing whether he is more afraid of an attack or a parry. This is much easier to handle than the many possible attack timings he could use otherwise.
Of course, he can block, but then your parry will be cancelled into shield pressure, your Down Tilt can be spaced safely, your Grab will outright win, and your Back Air can cross him up and set up a great situation for you where he is pressured to get out of shield and can't grab you. Spot Dodge and Roll can be covered in similar ways.
If he doesn't want to play this game, he can retreat, and if your opponent is good they'll know how to predict and properly whiff punish your moves, so your goal is to know what space he's going to defend, and when he's going to defend that space or give it up in the hopes that you'll commit before he does. If he is doing this, the space is yours, and you can walk him into the corner, or at least until he's not comfortable retreating any more, at which point you can read that and catch him. And because you are approaching, you have the luxury of choosing to stop if you don't feel safe. Marth does not get to choose whether or not you keep going.
On top of all this, running forward during the parry also has the advantage of causing Yoshi to slide forward during the parry and during his jumpsquat, which means that it is difficult for even Marth's long-range moves to outspace your parry. Even a tipper Down Tilt or Forward Air can be punished after a parry if you have the momentum from your run.
As far as jumping goes, you should always keep in mind that Marth wants his opponent in the air. This is where his moves have priority, can't be crouch cancelled or blocked, and where his opponent isn't able to dash dance. This is true for Yoshi as it is for any other character against Marth, although Yoshi doesn't have it quite as bad as someone like Peach or Sheik. If you think Marth is going to try to jump out of the corner, or if you can counter-hit an aerial, then short hop Back Air is great. If you can read Marth's Down Tilt, your short hop Forward Air will be very rewarding. Just don't play into his hand by being conditioned by his Down Tilt, because if you try to read it too often he can jump and swat your aerials away easily.
Wavelanding and other movement on the platforms isn't something I recommend against Marth, at least not as the main game plan. If you are cornered, or if Marth has managed to put more pressure on you than you are on him, it can be tougher to play the ground game, and in this case the platforms can be a safe escape. They can help you get out of a bad spot as long as you don't try to be too gimmicky and only play from the platforms. His aerials will beat yours easily and he can stay out of their range if he wants. You can also try to armor trade, but if you're able to do that, you might as well have made the same timing read on the ground with a parry, where you wouldn't have taken the damage. If you are above Marth, focus on getting to the ground safely.
Finally, if you do get in close to Marth, take advantage of his awkward frame data and weak moves by crouch cancelling or abusing your faster moves like Forward Tilt. Cross up his shield if you can.
For edgeguarding, double jump armor is great for protecting you when you grab the ledge against his recovery. You can try throwing an egg to grab the ledge and see if you like that instead. It can help cover a high recovery. Yoshi can do the Marth Killer but it is possible for Marth to avoid it, so you are probably better off just trying to edgehog him, and hit him back offstage if he lands onstage.
. but like you said the projectiles works well sometimes frustrating marth players cause of pressure. It's a hard matchup but a fun one with a even playing field.
