Gonna just reply to these in the same order.
1.Since blaster has been nerfed pretty bad, and Falco can no longer really camp or force approaches, the mobility issue is going to be most obvious if Falco cannot stop Diddy from getting a second or two to himself to pluck a banana when he wants. AFAIK, Falco will not be able to consistently stop Diddy from setting up his banana, either by patiently plucking it behind him and immediately jumping, z-catching, and fast falling back to the ground, or aggressively b-reverse plucking the banana towards Falco from mid range and approaching with fair, dash grab, nair, and empty hop mixups as the banana falls and traps. Diddy Kong is going to get one nasty mixup per banana that Falco can't stop Diddy from setting up. If Falco gets hit into the air he will probably get comboed for decades. I'l get into that later.
This is a lot harder to deal with than it sounds on paper. Even if you defend against the banana really well, say, by z-catching it and immediately throwing it away or back at Diddy, you're still being forced into a situation where you have to do something and the grab/fair mixup is on the way. It's like how Dedede mains use gordo, it can be defended against but you have to do something, which allows Dedede to come at you the way he wants.
Except Dedede's are explaining why Gordo isn't trash. Diddy's use this strategy to make bananas the best projectile in the game. There are dozens of of ways to approach with bananas in Smash 4 because now we can repluck a banana out of our hand after the initial spawn pluck, in addition to four directions to throw and a z-drop. Different setups require different defense maneuvers. Because the Diddy player will know which way he will approach out of many setups and the opponent has to guess or react, skilled banana approaches are the most free mix up in the game. And Diddy gets a lot of reward for getting in.
For this reason I don't think Falco's reflector will be very good here for anything other than pokes, unless he has a much safer one in customs because otherwise it's gonna get punished by something like jump to fast fall fair or nair too much if he tries to use it to reflect the peel. The risk isn't worth the reward because Diddy is ready to go for the follow up before he throws, z-drops, and plucks bananas at you in weird ways to trap you.
As far as taking the banana away goes, air speed is good but foot speed trumps it. Because a foot speed character can just sprint across the ground as far as he needs to before jumping and z-catching the peel if its in the air. Additionally "z-scooping," or z-catching an item that is on the ground, is now a thing. Simply running up as close to a grounded banana as you can without tripping and jumping with an immediate z-scoop is a fast, lagless way to pick peels up off the ground. But it's going to be a bad idea if you have slower foot speed than Diddy, because again, Diddy's entire playstyle now revolves around using bananas to force the opponent into situations where he has the advantage. He will use grounded bananas as lures and you will get faired if he catches you going for this.
Characters like Fox, Pikachu, Falcon, Sonic and such are good at taking bananas from Diddy off the aggressive pluck and off the ground for this reason. Falco probably cannot handle this situation like that. A Diddy who knows how to get the most off of every banana and setup as many times as he can will actually force an approach himself. Which he can also use to lure people into hits.
You're other option is to overpower Diddy's neutral by approaching while simultaneously destroying the bananas Diddy tries to pull out to set you up. Someone like Pikachu can do this well, destroying aggressive b-reverse plucks with jumping thunderjolts and fairs on the way in.
Can Falco achieve something like this? Is the front of your face safe at all during phantasm or will the banana hit you if you try to rush through it? Could blaster snipe bananas on the pluck safely? Because if someone did that to me more than once in a real match I'd probably freak out. Since the nerfs bananas are Diddy's everything. Diddy does pretty low damage and knockback now. He needs to be able to open the opponent up much more than they can stop him while dishing some damage back and the banana is how he does this. Characters who can take advantage of the peel's awful, awful durability and quickly destroy it should figure that out.
2. If "Falco's probably not going to be able to do much at disadvantage against anyone; his only hopes are death and someone being stupid," you're probably going to lose this matchup hard if you have no way to disrupt Diddy's nuetral. Like, 7-3. Since the patch Diddy is like he was in Brawl: a relentless combo maniac with a dozen hits at a good advantage and a million ways to open you up in neutral. This is gonna be made way worse by Falco's issues at disadvantage as Diddy will get more damage per power play than usual. Which will add up really fast.
3. But also like Brawl Diddy, as of the patch Smash 4 Diddy's Achilles heel is the fact that he has terrible kill power outside of hard reads and pefect banana setups. He has reasonable moves for this though, in his F-smash which is now only a little bit more unsafe, and the second hit of his D-smash which is actually quite powerful. With customs on rocketbarrel attack is a risky yet brutal coin flip mixup that will destroy people early if Diddy can bait an air dodge, but Diddy will get hit if he misses, especially by fast fallers like Falco.
If you can avoid these three things and draw stocks out for as far as you can and use your superior kill power to close stocks before Diddy lands his kill you can be successful. Even if you take a slight beating in the neutral.You just have to stop as many banana power plays as you can.
Bair becomes a kill option near the edge for Diddy at around 130% I would imagine? Watch out for bairs and dtilts to bairs at that point. U-tilt can be a good kill option at higher % but maybe not as much vs. Falco.
4.Okay, I think we can comfortably say that Falco can gimp Diddy by taking his barrels out when he is forced to recover low due to his ability to go deep. But a lot of characters can say something like this, the hard part is actually blocking the monkey flip to the point where Diddy is so low he has to charge barrels to recover. Monkey flip is fast, so this isn't easy. You will have to be either really on point with your wall of pain or find a more creative solution.
What I've been practicing is using Pikachu's B-reverse thunder just off stage to create a disjointed wall which will block the monkey flip from reaching the ledge and force Diddy to charge the barrels low where he is easily gimped by thunder jolt and quick attack.
But even that's hard. Monkey flip is a fast, safe, and confusing recovery since Diddy can wait to leap halfway into the stage and back to neutral where he dominates for as long as he wants. Coupled with the fact that the peanut cancel makes his movement even more crazy, I don't think most characters will be able to stop this recovery enough to put Diddy under the stage where he's screwed.
But I actually think Falco might have a shot if you can make some reads due his godlike jump speed, his godlike jump height, and Wolf's bair. See if you can wall of pain Diddy with bair to the point where he has to charge barrrels from below the stage. Then go deep and tap him with whatever. If you can get one good early gimp 2 out of 3 games it could salvage the matchup.
One more general thing, all characters have the same item fundamentals, so learn them. Practice, z-catches, z-scoops, and if you really hate Diddy learn how to use aerials with a banana in hand by z-dropping and immediately catching with the aerial to keep his banana away from him for longer. Falco mains will have to come up with a great game plan and then iron it down to a fine point as Diddy is still a force of nature but this doesn't have to be unwinnable for Falco.