1) Yes, it will activate.
Smogon doesn't allow you to use anything on their PO servers that you can't use in-game. If you can't have two Kyurem alternate forms on a single save file, then you can't have two Kyurem alternate formsforms on your PO team
2) No, it will NOT activate.
- Pretty much the rule is, you cannot have two Pokemon with the same pokedex number on the same team.