The reason/reasons she keeps him in the basement (mostly over night) is to keep him from jumping up on the kitchen table, sink, to keep him from running up and biting her or whoever and to keep him from getting into "things" in the house, (nick-nacks) etc.
Cindy,

I think your mom needs to kitty proof her house. IMO, and I don't mean this with any disrespect or to offend anyone, I don't think it's fair to the cat to be kept in a basement. And it COULD be the reason why he's doing what he's doing.

My cats are free to come and go as they please (indoors only). If they climb, they climb. Cats like high places. I have two cat trees that they love, which keeps them busy and away from places I don't like them to be. Maybe if your Mom got him his own cat tree, he wouldn't jump on the kitchen table, sink, etc. It's not to say that it doesn't bother me that my cats jump up on the table and counters, as they are cats and their curious. But I clean like a banchee and make sure I have plenty of disinfectant handy.

I wish you guys luck. I also ask that you be patient with him. Give him all the love and time that you can. Too many people are quick to give their pets up (not saying you) for these reasons without first taking the time to find out why.

An excellent book to read is "The Cat Who Cried for Help" by Nicholas Dodman, DVM. It might help explain things a little better than I can.