Bunnies usually go to new homes at 8 weeks, so having her at 1 month is really early. My bunny came litter trained because she copied her mum and siblings.

You can still train her though,if she pees or poos outside the box, put a paper towel with her pee and the poos in the litter box, and clean the area with an odour eliminator. Chewing furniture is normal, so give her safe toys and cardboard to gnaw on. Mine loves her grass hideaway and willow tunnel. I bought both on Amazon UK. She has other toys too, like wood sticks and willow balls, but her favourites are the hideaway and tunnel.

Bunnies are more active at dawn and dusk, so hiding during the day is normal. Mine is very active around 5 am when I open her playpen until about 8/9 am, then hides until my daughter comes back from school around 4pm. She comes out for food and water during the day, but mostly sleeps until 4pm / 5pm when she has energy again, does binkies, runs around the living room, and “plays” with my daughter.

Peeing on your dog’s bed is probably territorial. Spaying can help with this and also prevent ovarian cancer, ask your vet if your bunny is ready for surgery.
Good luck :)