Yes, this is necessary for house rabbits. Not trimming a rabbit's toenails can cause sore hocks, where the fur on the hocks gets raw and sore and in an extreme case infected. If your rabbit does have sore hocks, make sure it doesn't sit on cage wire all day. I've used drywall but some experienced caretakers caution against materials present, per comment kiln-dried pine wood or white wood is good. Cardboard will not hold up.
Re. clippers, yes, the same will probably work. But just some "common sense"-type advice:
- the clippers should be comfortable for you. Even if cat clippers work fine, you may find them too big, for instance.
- any clippers can become dull. If the cut is not clean - i.e. the blade goes past the nail, then it tears forming something like a hangnail - that's bad. You'll need to replace the blades or clippers (or sharpen the blades if you can figure that out.)
As for clipping nails in general, for light-furred rabbits it's usually easy, as much like human finger nails you'll be able to see very clearly where the blood starts. Clip above that, try not to get any fur, you're done.
For darker furred rabbits there's a good chance you'll be able to see anyway. Good light will help. Otherwise, in the worst case you may have to use some estimation and guess work. Rabbit nails shouldn't really curve (if they look like talons they are way too long), so you can cut off the curve or sharp point. You'll try to get an intuition for the thickness of the real part of the nail.
Obviously this bit about guesswork if you can't fully see where to cut is uncomfortable. Yes, bleeding may occur. This is obviously undesirable but straightforward to deal with - you should have a clotter, such as cornstarch or a commercial formula, on hand.
Lastly, front feet have 5 nails each (4 + a thumb), back feet have 4 nails each. Cavies are 4 front, 3 back, for reference.