The games are so easy it doesn't really matter if you use multiple of the same type, though! Although even knowing this it's just something I never did, haha. I did have the issue of wanting to use the red Gyarados as well after I'd picked Totodile though.
The elemental punches are pretty cool, but they're frustratingly inaccessible for the majority of Pokemon that can learn them because they never seem to be part of a Pokemon's moveset by level up, and things like move tutors and heart scales always seem to be quite scarce until the endgame. Or worse, they're egg moves and you have to go through the tedious process of breeding for them. Maybe I'm just impatient and don't like putting the work in when I don't have to in order to beat the game, though! Running multiple type moves on a single Pokemon is always fun, though...at least when said Pokemon will allow you too. In a lot of my playthroughs I find I have multiple moves of the same type and that bugs me too. xD
I seeee. Yeah, I found Black 2 much more enjoyable than Black, if only because of the PWT and because I didn't have to use trashy Unova Pokemon only. Are you playing a ROM or an original version? If the latter I'd say just get Dream Radar, put your cartridges of previous games in, and go through it with Lugia/Ho-oh/Dialga/Palkia/Giratina for laughs. Did you ever do the Arceus event in HG/SS? Running around with a Level 1 creation Legendary was ridiculously fun, haha. I replayed Yellow a couple of years ago, if you go through it now then good luck to you - it hasn't aged as well as it could have!