1. Do you always fast expand? More specifically, is there a solid way to fast expand in ZvZ?
2. What do you do vs those f*cking protoss 4gate assholes, I mean how do you detect & defend it without messing up your own build? (I can hold it off most of the time but doesn't exactly leave me in an advantageous position)
I always fast expand even in ZvZ. It depends on what league you are in definitely. When I've done coaching previously, I've always told my pupils to FE in ZvZ however you do sometimes run into the chance of getting 7 pooled or 10 pooled. With the new maps though this usually isn't an issue as long as they don't scout you too early, which if they do you most likely want to cancel. The third base in most ZvZ is often the trickiest to get which is why you see a lot of 2 base roaches play. From there I either instruct them on how to do multiple roach timing attacks with potential Hydra follow up or if they are more comfortable with spell casters to use infestors. Mostly in the lower tier I focus a lot on scouting and how to utilize that information to succeed.
As far as four gates I really don't see many of those after the nerf. Most PvZ I play they FE with a forge or gateway. However in lower tier games I do see them, most times I instruct people to cancel their third, put up spine crawlers, get a roaches if they don't have them and you should be fine. If they don't expand behind it and you hold you just flatout win. If they do expand behind it you can either out macro them or just crush them usually.