Stuff posted by others is useful. If it wasn't mentioned, Pikachu has the best spot-dodge in the game (tied with Falco and I think Yoshi/Link/Toon Link, not positive on those last 3) so that's usually preferable to the slow roll, although Pikachu's roll can still have uses.
Also, look into your respective main's specific forums (in this case I'd guess Pikachu, same main here). There's tons of specific threads for advice for dealing with various characters, and tips and tricks characters have to deal with other characters and for general use.
As a Pikachu, based on your description of rolling, down-smash less. If you play a good player, they will escape it easily, and while it's very rare you will actually be punished for hitting them with it, it will not KO them and if they get used to it they simply shield it and hit you with often very strong attacks. Down-smash has uses (some of which are in Pikachu forums) but as a general purpose move it's somewhat lacking.
Also, don't fight level 9s much [or AI in general]. Some people have AI levels that are okay for sparing with (I think some people really like level 7 Snake or level 3 Meta Knight) but level 9s are way too predictable. For kicks and to prove this point to someone, I three-stocked an AI MK level 9 and took less than 60% - as Ike. They have obvious habits that you can exploit but when other people act differently you'll miss punishes and eat damage.
More general advice for competition:
It's early to do so now, but in like 6 months or whatever (maybe way less, maybe more) you should either start considering a backup or really practice (for Pikachu) Ice Climbers, Olimar, Marth, and Lucario. It goes without saying that every character should practice Meta Knight, but those are harder (in Olimar's case very tricky) matchups and you either need to be prepared for a rough fight in tournament or else have a secondary character (in this case Zero Suit Samus and Marth improve every one of those MUs for Pikachu by at least +1) to deal with those characters (and also in that case practice the backup vs MK matchup too because people have backups to deal with someone else's backups). Some people have 3 characters, but that's a stretch and I wouldn't think about it unless you fall in love with Pikachu and Falco or Pikachu and King Dedede so that one character (for this example, ICs) still gives you issues.
For practicing chaingrabs (Pikachu has them and learning them is worth your time), DON'T USE TRAINING MODE - stuff doesn't stale in there properly (I assume you know what I mean, if not find out what "Stale-move negation" is) so CGs on Snake and co. don't work right. Whoever it was above that posted to practice them in there might be right about Melee, but I've seen and read and tried and moves don't seem to stale in there. Instead, go to multiplayer, turn all items off, and turn on another player by just leaving a controller plugged in/on and make it an endless KO fest (time mode, time set to none). You can CG them to however high (and KO if it's a zero-death), then jab them a bazillion times (or dtilt or whatever) to refreshen all your moves and start again.
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Short story: others are right, character-specific forums are useful, dsmash less, AI aren't that good for training, practice hard matchups or get a backup(s), don't use training mode for practicing CGs.
EDIT: Also the best advice to date was given by Isai [brackets are my addition]: "Don't get hit [or SD]." Because if you don't, then at the end of 8 minutes, you won or tied, but either way, you can't lose. Really then, the rest of the game is just execution of that idea, and trying to make your opponent fail to execute that same concept.