Pokemon Seventh Generation – Can Pokemon Hit By Fire Fang Get Both Effects At The Same Time?

Yes, the Move Reminder will teach you any moves that your Pokémon either knew previously or had the opportunity to learn previously.

From this page on where to find the Move Reminder:

The move reminder is the more useful of their pair of NPCs since she lets you re-learn any move that your Pokemon either learned at an earlier level or had the opportunity to learn at an earlier level. This includes moves that have been inherited by eggs which is especially handy given that Pokemon can learn additional moves they can’t anywhere else via careful egg breeding.

As to where to find her, from the above page:

The move reminder NPC is found fairly late on in the game for such a crucial area – she’s on Ula'ula Island’s Mount Lanakila. This is a place you’ll only visit once you’ve completed all the various parts of your island trial. She’s next to the shop inside the mountain’s resident Pokemon Center.

No, that is not possible. You may use Pokebank from next month to transfer between generations like in the link you posted, but XYORAS wonder trade is separate from SM's.

Here's a source