how can i sell the dog (or give it away, or get rid of it)?
get rid of it = don’t feed it anymore.
ouch, that seems too harsh… guess i’ll keep it 
I’ve only had the dog and fish so can’t say about the other pets and AFAIK there’s no options except starvation.
Still, the dog stops the home being burgled 
Well, the hamster can die for no good reason (no, there was enough food, so he didn’t starve). It already happened to my latest character twice. I guess she’s unluky in picking healthy hamsters as pets. ^^
Her cat and fishes are fine.