Honestly I have a pair and they are constantly pulling up the carpet, its just part of a natural instinct and some rabbits just enjoy it. As for pooping, its really hard to control that, rabbits poop about 300 times a day so leaving them out there is bound to be some poop.
Some basic potty training tips are, find where they poop and pee, then put a litter box there, once they are using that for a while, slowly move the box to a more favorable location.
Alternatively you can get a collapsible fence and have that up when they aren’t in the cage, it limits their area but still can give them room to exercise, it also allows you to put towels down to prevent them from getting to the carpet. You could try putting down carpet samples (like 2’x2′ and see if they go at those and leave the real carpet alone.
Honestly, I’ve just given up on my security deposit and will replace the carpet when I move.
an example of a pen: https://www.amazon.com/dp/B00377WL46/
Some brands you can chain together so you can get multiple and combine them. 24″ tall should suffice for most rabbits.