Well, my answer to this is how long of a reply do you want? I'll just go down your questions in the order you posed them.
How to Play Roy
This could be dependent almost entirely on your own playstyle if given any other character. Roy however is not like any other character. He has very glaring weaknesses that almost automatically put him at a disadvantage to the rest of the cast. To play Roy optimally you need to have a resounding knowledge of the game and different character weights. Roy is like the character you pick to handicap yourself when you're playing against someone who isn't very good.
Be prepared to L-Cancel. A lot. Practicing SHFF-F'air-Lc [short hop fast fall, forward air, L-cancel] will make you inherently better with Roy. You will need L-canceling if you expect to do anything with Roy, his moves do not have enough hit stun in the air for you not to use SHFFLc on any of your aerial moves, the only exception to this that I've found is Roy's Neutral B. (Which in my opinion is one of his best moves.)
In my case I have to actually move much faster playing as Roy for the same outcome as say Falco or Fox, I can average 230apm with Falco and do fine but not nearly as much with regard to Roy.
Roy's moveset can go one of two ways IMO which is only an opinion; You can go all ground using your tilts and f-smash and B moves. Or you can go for a mix of Air and Ground. This is where you see people give up on Roy when they hit someone with their F-air and nothing happens, or they hit with the First hit of N-air and nothing happens and your opponent can simply smash you away.
Roy's Aerial moveset is not made for KO'ing. Once you understand this you can now move forward.
Combo lead-ins with Aerials: SHFFLc Up air into grab, into down-throw, into F-smash if your opponent's DI fits. If DI was mixed up follow up into SHFFLc F-air into D-tilt into F-smash if DI fits.
Second hit of N-air into an L-cancel wavedash, into a smash.
There a ton of things that you can do with Roy if you're willing to put up with all of his messiness. Or if you really want to be that guy, just walk around and F-smash. However, once you learn advanced techniques he becomes a lot more than just F-smash.
So a key to playing Roy is to learn how to L-cancel all of his aerials otherwise be prepared to be punished hard. Like super hard. Zero to death kind of hard.
Optimal Stages
Yoshi's Story is his best stage. I don't feel that I need to explain why besides that he can kill easily on the sides with F-smash at around 60%.
Fountain of Dreams could be considered his next best stage. I however do not have good luck with the stage.
Battlefield. Once you learn how to sweetspot the ledge on this stage it could easily be one of his best stages, I have way better luck with BF than with FoD.
Final Destination. If you learn to chaingrab Roy on FD is far more dangerous than he normally would be.
These are the four stages I consider to be his best, however I do not speak for every Roy player. These are just the stages I have the best luck with.
Match-Ups
Samus: Don't play this MU. It's bad. So painfully bad. Hurts my soul.
Fox: Not as bad as you might think unless you get shined from one end to the other, Roy's D-tilt leads into some really hard hitting moves.
Falco: Very do able as long as you don't get pillared and even then. Hardest part of the MU for some players are the lasers, however this is more of a global problem than just Roy. It's fine to get hit by the laser, but don't get hit by the move after the laser.
Sheik: Ow. Pray the Sheik doesn't know how to chaingrab, and once that prayer goes unanswered and you get chain grabbed do your best not to get F-air'd into oblivion, use wavedashing into D-tilt and you should be okay for the most part as long as you follow up. Try not to use F-air as much in this MU as Sheik can N-air out of pretty much any of your aerials.
Peach: This is not an easy MU, maybe even harder than the Samus MU if the Peach player is good. Don't meet with F-air again in this MU, rely on other moves once Peach is in the air, her N-air will destroy you after you hit with F-air. Second hit of N-air is a good choice, but only the second hit.
I'm not going to go into every MU, there's already a MU list somewhere around here.
Essentially if you don't learn any advanced techniques with Roy don't be surprised if you get destroyed at high level of play. L-Canceling is a must IMO.
I could write more but my thoughts are kind of scattered.
