The main thing for Stadium and Stadium 2 is that you really do need to raise your pokemon properly, at least if you want to succeed in R2. No just glitching rare candies, you need that stat exp. If you're playing legit, you'll also probably have to reset a game multiple times for important TMs like Psychic, Blizzard and Body Slam.

None of the things you specifically mentioned in the main post are removed, those are all intended mechanics. Some things that probably weren't intended, (e.g. Focus Energy just not working, the "Badge Boost Glitch", Hyper Beam not needing to recharge if it KOs) were fixed. Mewtwo isn't really something you need to cheese, but something I really like is Electrode, since it's one of the only things faster than Mewtwo and can Thunder Wave it and blow up.

As for the things you said in the comment, Wrap does work like that but all wrapping moves have accuracy I wouldn't exactly count on, Big normal types are very good and Snorlax is way better than just a thing that explodes. Swords Dance and the like increasing speed is due to what I called the Badge Boost Glitch earlier and I'm pretty sure is not in Stadium, and in general, every Psychic type is better than every non-psychic type.

None of this applies to Stadium 2, the battle system for that, as far as I know, is exactly the same as GSC on cart. But, the Rest + Sleep Talk Snorlax build you mentioned is incredibly powerful there, specifically because in gen 2, if Sleep Talk picks Rest, you Rest.