What might these growths be? and removing harmful crabs.

[untamed]

I always give the critter the benefit of the doubt before removing it. I wait to see if I can see any kind of damage before I act.

However, having had the same kind of crab that you describe create a nice dead spot in my SPS, I removed him with a pair of sharp nosed tweezers. I created a frag or two in the process.

I doubt that a crab of that type will leave the coral to fall into a trap.

As for your first photos...I agree...sponge and valonia algae. Valonia has certainly given some people trouble, but it has never caused any problem for me. I think that people get into trouble trying to eliminate ALL algae from their systems.