Some notes to answer these questions:
Falco was moved over Fox solely because of his reflector (not the shine hitbox, the actual reflecting capabilities). He does not experience any lag from reflecting, so he can reflect a projectile and jump out on the next frame. This is an unintentional side effect of the way his shine was reprogrammed from its Brawl version, but it has not yet been fixed.
MK is really good. The short version is that he's basically a more aerially mobile version of Marth with better killing and gimping capabilities. Bair lets him kill well in the air, his fsmash and dsmash are really fast kill moves, he has a pretty good recovery, and can continue combos very well. I moved him above Marth in this update because I realized that his range is actually deceptively long and he is better at continuing combos than I had previously realized. His tiny hurtbox also works really well with his disjointed hitboxes to keep him safe.
I've talked a bit about Peach before. Peach and Sheik are super close and switched positions on this list, and it could certainly be the other way around. However, since so many characters have way better recoveries and can therefore gimp much better. This makes Peach's recovery capabilities more valuable, and also makes Sheik's gimping capabilities less effective since characters are able to recover more successfully. Peach is also a lot better at exploiting PM's inferior shields than Sheik is, since Peach has amazing shield pressure while Sheik generally just has to grab you if you're shielding. Peach also did get some explicit buffs in her up tilt, side b, and I believe up b, but the main thing is just that Peach does better in PM because of the improvements the cast received and the altered shield mechanics.
Pikachu's placing is primarily due to his new QAC and moderate buffs to other moves. I don't have too much proof that I can provide for Pikachu since there aren't many high level Pikachu vids out there. However, having played Axe's Pikachu and seeing how powerful QAC is even with his limited PM experience makes me pretty terrified of Pikachu. He doesn't have amazing range, but he has good combos, good killing power with his smash attacks and bair, down b is actually good in this game due to its very low endlag, and he is still great at going way off stage to gimp and then recovering with his excellent up b. Just for reference, Pikachu was already 10th on the most recent Melee tier list, and was substantially buffed. QAC just gives him absolutely ridiculous mobility and his improved moves make him more solid overall.
Game & Watch is one of the most underrated characters imo. I gave a brief overview, but really he is just super strong and has good combos. You can land cancel his neutral b, which lets you create walls of food that help keep him safe, and the pan hitbox sets up for lots of stuff since it has no extra landing lag. His dash attack can be cancelled into grab and up smash. DA -> grab is really good on shield and works on hit at low percents. Dash attack to up smash works at mid percents and kills really early since his up smash is so strong (like you can kill after connecting with a DA at about 55-65% depending on character on most stages). All his moves are also disjointed and have really high priority, and do lots of damage and knockback. Fsmash does up to 38% if all the hits connect and just destroys shields. The ability to jump out of up b is also super useful for continuing combos and up b is excellent oos (I assume it still comes out on frame 1, but I haven't seen PM frame data to confirm). Game & Watch basically has all the qualities that make a good character other than a shine. I think G&W is good enough that I am probably going to pick him up in addition to my other characters. I currently play Fox, Falco, Lucas, Wolf, and Peach if that gives any indication of how good a character has to be for me to play them.
Zelda is also really good, but just not quite as good as G&W. Her recovery is long, but not very safe. Her neutral game is also somewhat limited due to her lack of persistent high priority hitboxes. Aerial neutral b is really good and sets up for lots of stuff, but it's kind of predictable and not always viable since you have to jump and wait a little while before using it if you want it to land cancel. Din's fire is also good, but can be neutralized fairly easily by hitting the fireballs. She's obviously pretty good, but I think she's somewhat outclassed by the characters above her.
Ivysaur seems better than Zelda for several reasons. Razor leaf has great range and hitbox properties. All of Ivysaur's moves also have good range, she can heal herself, has very strong combos, one of the best recoveries due to how safe it is, nair is incredibly good, and Ivy has good killing power and gimping capabilities. This is not too in depth, but I think she is better at these things than Zelda.
Diddy is low just because he doesn't seem to have any outstanding strengths. I'm honestly not very sure who should be in the bottom 5-8 characters, since PM really is pretty well balanced. Diddy has decent combos and an interesting banana game, but his combos don't seem to be all that great compared to the competition. His recovery is also pretty predictable, which is an issue even if his barrels hit you when you're trying to edgeguard him. So far he's just the least impressive to me, but I'm not super sure about his placing.