It’s always wise to have a girl rabbit spayed. Girl rabbits have a high risk of developing uterine cancer around age 3-4. Spaying can also help make a bunny less stressed.
She might still be missing her friend. Rabbits form very close relationships. If she’s feeling lonely, she might want to be in the bed because it’s soft and has your scent on it. Sometimes however a bunny who loses its friend become more “free” in its ways and more bold.
It’s very difficult to dicipline a rabbit. It doesn’t really work, because the bunny tends to associate the punishment with the person who distributes it, rather than with the forbidden action. The best thing is to try and block her access to the bed. I’ve done that with my bunny and my sofa – after a month or so, he’d “forgotten” about the sofa, and I could unblock it without him trying to get up on it.
Eating garbage absolutely can influence her poop. Small and black is not good. As a rule it means the bun is getting too little dietary fiber. She should eat lots of hay so her poop gets big and golden-ish. Here’s a guide to bunny poop: http://imgur.com/a/5N4lD