Their feet should be attached to the gliding membrane.

Nails can be trimmed, but not to short. It's good to trim them, but its hard to do alone. It's good for you & them when they are trimmed so you know they wont get caught on anything & they wont scratch you as bad.

They can grasp things really good, but the nails do play a big part in how they can climb. See what way works for you.

Another thing about their nails is that the scratches will itch, it will go away, & you do become kinda immune to it throughout time.