Is your basement like a den/living room area? The basement might be too cold for the pigs to play in, but it sounds as if your basement is a den/living area if you have carpet and furniture down there.
For the wires you can get some molded wire covers at home depot or the hardware store. They cover up the wires and blend in to the paint so its not ugly. You just have to think of safety for the pigs as baby proofing your house, just as if you had a baby that you didnt want to get into anything.
As for the carpet, you can get a shower curtain and lay that down on the carpet, that way when they do pee and poop it wont wet the carpet and its easy clean up. I have carpet, but I don't use a shower curtain, I use fleece. The pigs relate the fleece to there cage and pee and poop on the fleece. I put the fleece in a cat style bed and put that on the carpet, and kinda just time it out when I think they are going to pee. I take them and put them into the bed where the fleece is and let them do there business and sure enough they pee. Then I take them out of the bed and let them play on the carpet again. I keep doing this until floor time is over.