Maybe, it’s possible the other molds would just spread to another location in the house. You would also need a particularly genetically hardy sample of oyster mycelium. Many of the times I’ve tried to grow mushrooms the mushroom was out competed by wild fungus.

Yes. Potentially. Although this is more likely to occur in a closed environment.

Tasty, too

Get one sometime, and cook it with rice. You won’t regret.

(Seriously, it’s edible and good)