What might these growths be? and removing harmful crabs.
 

The first pic is a sheet of fungus or something growing near the base of my Green Paly's. Should this be a concern?

The second pic is a growth on my LR right near bird's nest coral. It may be nothing, yet I don't know. It is round and appears almost like a bubble or marble. Any thoughts out there?

Also, on the bird's nest, I have 2 resident crabs that came for who knows where. I think the symbiosis is cool, but am told they have to go. Is there a trick to trapping them? or is a pair of tweezers the only way to go?

the first pic looks like a sponge of some sort while the second is bubble algae...maybe valonia.

I wouldn't remove the crabs if they aren't causing any visible harm....especially if you think the symbiosis is cool...

where and why were you advised to remove them?

What do the crabs look like?

Should have mentioned the crabs resemble small tirantulas
 

hairy legs and eyes spaced far apart. There are 2 smaller ones that live on the birds nest and one much larger one that is very evasive. LFS has said to fluch 'em if caught - don't know how to catch these guys without damaging the coral. The damage they are doing is debatable as is kida tough to tell at times.

Sponge and Villonia. If it was me I'd banish the crabs to the porcelain aquarium.

I would get rid of them, or a better solution (for the crabs anyways) would be to put them in your sump (if you have one). It certainly doesn't hurt to get rid of them, especially if you are not sure if they will be a pest.

One trick to catching them is just to put a glass leaning against the rock where the crabs hide, and put some food to attract them in the bottom of the glass. Crab goes in to get the food, but the glass is too slippery to get out. Sometimes it works, sometimes it doesn't.

xanthid crabs no doubt, eliminate them!

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.

the larger, evasive ones are likely worth some skepticism, but the acro crabs are very likely a symbiotic species and it would be a surprise if they were detrimental to the colony they have evolved to mimick...

Most of the nice acro crabs aren't hairy...