Dump of personal notes that I thought were worth noting. Some (or all?) of it may be known, and I wouldn't know because honestly I don't really keep on top of what everyone else it doing.
If you manage to catch HW after it has hit someone (most easily done by first using down-special, having it bounce off the opponent's shield, catching it before it lands, then z-dropping it on the opponent as you land and re-catching the HW again; still with me?) the very next time you throw HW and it hits someone it will have already exhausted its hitbox and will instead immediately burst into flame upon touching the opponent. This obviously makes it extremely useful against aerial opponents, e.g. giving you a free Dair spike off-stage, so maybe consider holding onto it using ZAC and IZAC techniques combined with specials to potentially get the opponent off-stage before you throw it away in these instances.
If you're concerned about HW being shielded and then creating a hitbox on the ground that hurts both you and the opponent, buffer it out of a FH (or higher up) and it will run out of active frames and disappear before it touches the ground, then you can proceed to ignore it (or catch it if you wish).
I found two buffered setups that allow you to consistently make the HW land on the edge of the stage, burst into flame and then slowly fall past the ledge.
1. Ledge jump buffered horizontal directional airdodge towards centre-stage, turn around, then SH buffer down-special.
2. Get to the edge of the stage facing out (e.g. Dash/Run into the edge), stop, Jump directly up and buffer a directional airdodge back towards centre-stage, then SH buffer down-special.
Being able to consistently set this up is sweet because it can 2-frame recoveries and then if the opponent is caught in the flames off-stage you can get a Dair spike kill out of it.
Diagonal-down Fair/Bair cannot be FF'd until frame 3, and unlike with other aerials the FF cannot be buffered or held before/as you A-stick an aerial to have it automatically FF. So no, it's not you screwing up.
This is just a personal preference thing, but after giving A-stick Diagonal Fair/Bair a good go, I cannot overlook the added consistency that using the joystick for diagonal aerials provides, especially for using diagonally-down Fair/Bair off-stage.
Diagonal Fair/Bair have different tether areas/ranges to normal Fair/Bair tethers. And by different I mean holy ****, you would be surprised by how far up you can be and still have Diagonal down tether the ledge, and vice versa. Speaking of which,
Have you ever tried to tether the ledge, and you swear you were in range because past experience tells you it should have tethered. but it just didn't? And no it wasn't because you had been hit recently, or because you had recently been on the ledge, and it had nothing to do with grabbing the ledge too many times. You were in range, you tethered, and got nothing.
What if I told you, that for some reason (I can offer explanations, but it doesn't matter), the area within which you can be when the tether wants to come out to grab the ledge, is different depending on whether you are falling or not. I'm talking about a difference that I have tested and demonstrated to be at least 24 tiny training room squares of vertical height (same horizontal positon) on the frame the tether tethered, or in other words that's 2 and a half of the slightly bigger squares; certainly big enough for you to feel like you've definitely tethered in that area before and had it work, only this time it didn't, and hey maybe you were FFing, and had no jump, so maybe you're dead now.
Point is, when tethering to the ledge out of a FH or DJ, you can tether while rising or at around the peak and you'll be able to tether the ledge really far beneath you with a diagonally down Fair/Bair; but when you're falling down (say if you got hit off-stage and you decide to FF then tether) just be extra careful about delaying your tether slightly so you are more in line with the ledge as the tether comes out (anything around SH height as the tether comes out is likely to fail so not worth the risk).
Note that this sort of difference (at least a notable one) doesn't seem to apply to tethering diagonally up when falling compared to out of a DJ (which there are also potential explanations for, but that's all just theory at this point and doesn't really matter).
You can hit and hold up on the joystick the frame after starting a Fair/Bair (or on frame 3 of Uair) and if the aerial tethers the ledge you will buffer a reel-in on the first possible frame, making it consistently very quick. Note that you must let go of the A-stick to allow Up on the joystick to reel you in, so flick the A-stick and then hit and hold up. (Holding the A-stick doesn't seem to affect hitting down to cancel the tether though, for 'reasons').
U-throw is now your combo throw, and you can forget D-throw unless the opponent's recovery is particularly gimpable or the opponent's character has specific defensive options which don't allow any room for missing combos. Why? Because U-throw will always give you more damage regardless of percent if you do the right thing, which isn't difficult to do at all. U-throw itself deals more damage than D-throw and then at its most basic it will lead into the same damage follow-up.
'U-throw to buffered SH Uair' (at very low percents only depending on the MU) and 'U-throw to buffered FH then timed Uair' are your new best friends. Go learn the timing of the buffered FH to immediate Uair; you can hold the jump during the U-throw and then it's the same timing every time for the Uair, and there's always a nice visual and auditory cue when U-throw's whip connects. You'll need to learn it because beyond very low percents, this is what you'll be using primarily right up until kill percents against some characters (for other characters you'll want to start doing DJ Uair or hoping you get a grab on a platform).
Unless they're at around mid percents, the FH Uair isn't going to combo, but it will cover every option that doesn't use an airdodge.
You have plenty of time to react to their DI and FH left or right to follow them, then Uair reaches so high that their DJ won't be enough to escape, and their aerials will either be out-spaced and/or out-paced.
When they do airdodge you can punish with e.g. landing Nair to re-grab (for normal airdoge), d-tilt or DA (for directional airdodges if pressed for time), or DJ aerial (if they go to a platform).
If Cross is used at the start of any jump, it will increase your vertical jump height, and if used out of a FH or DJ you can act soon enough that it increases your overall vertical potential. You must actually throw the Cross; an empty throw will not help. As for how this is supposed to help, well at first I thought it could aid vertical recovery in some cases, but that's wishful thinking as the two can't be buffered together, so I'm not sure.
One final note, let it be known that DJ Up-B gets you slightly more vertical recovery than DJ Uair-tether. (I'm only combining these options with DJ because that gives Uair tether the best possible scenario to prove itself by letting it wind-up and then be used at the peak of the DJ). In most cases you'd be using either Up-special or diagonally-up Fair/Bair (which both reach impressively high up). Considering the Belmont's poorer air-speed this will typically make Uair-tethers redundant.