Regarding Double-typed attacks:
I think, if they were to implement it, it'd have to follow the following guidelines:
1) If a Pokemon is immune to either type of the attack, they are immune to the attack entirely, even if they are 4X weak to the other type
I agree entirely with this. It would be consistent with the way type effectiveness works currently, e.g. Swampert is immune to Electric despite being half Water.
2) STAB would only apply if the Pokemon shared both types with the attack, and would be 1.5X. Alternately, STAB is +.25 for each type shared (so Vaporeon or Dugtrio using a Water/Ground attack would do 1.25X damage, but Swampert would do 1.5X).
Yeah STAB should not provide a boost greater than 1.5x, but I'd rather see STAB get nerfed in general, meaning single type moves only get a 1.25x bonus also.
3) Weakness and resistance are cumulative. Yes, this means Magcargo would be 16X weak to this hypothetical Water/Ground attack. But the same attack would be Neutral against a Water/Electric type, as Water would resist water and ground would be super against Electric. 2X*.5X = 1X. A Fighting/Electric attack would be 2X effective against Gyarados.
I agree that they should be cumulative the way you mentioned, but I think having weaknesses and resistances greater than 4x to be a little extreme. I wouldn't see too many problems with capping the effectiveness at 4x, much like how it already works with stat modifiers.
4) Dual type moves should be very limited in number (no more than 1-2 per type combination, and maybe for 10-15 total type combinations), fairly limited in availability (as in not a lot of Pokemon could learn them), and capped in power below the level of highly competitive moves. Some good examples, using existing moves:
Dragonbreath becomes Dragon/Fire
Muddy Water and/or Mudslap become Water/Ground
Elemental Punches (Fire Punch, Ice Punch, Thunder Punch, Sucker Punch maybe, Shadow Punch?) get Fighting type possibly added. This might warrant the introduction of alternate Physical options for some of these types.
Steel Wing becomes Steel/Flying
I don't see why they'd have to be so limited in number at all, nor the reduction of power. Dual type moves may sound very powerful at first, but they wouldn't be if you think about it hard enough. You're actually more likely to lose type effectiveness and get walled more easily. For example, let us take a Ghost / Fighting attack (Shadow Punch perhaps). Two types that have perfect neutral coverage and hit 7 types super-effective as a two move combo would actually be pretty garbage as a combo for one move (2 immunes, 3 resists and only 2 weaks).
I sort of agree with the limited Pokemon idea though. The biggest potential dual-type moves would have is to provide a wide variety of niche coverage on movesets. It would potentially open up a lot of opportunities for quirky (semi) exclusive moves that only very specific Pokemon learn, thus giving them another specific niche. I honestly think it would be a cool concept for Gamefreak to explore, though I still heavily doubt they would. As long as they do something equally radical next gen...
Anyway, other cool examples from existing moves:
Draco Meteor: Dragon / Rock
Seed Flare: Grass / Fire
Elemental Fangs: x / Dark
Silver Wind: Bug / Flying
Ominous Wind: Ghost / Flying
Drain Punch: Fighting / Psychic
Heat Wave: Fire / Flying
Twister: Dragon / Flying
Octazooka: Water / Poison
Ice Ball: Ice / Rock













