My rabbit Bobby is free roam and sometimes he comes downstairs and sometimes he doesn’t – I wouldn’t worry about it – she’ll roam around when she wants to.

Pretty much normal.
My rabbit does pretty much the same thing. (We close the hutch at night just in case) other then that we open everything to her. Most of the time it is in the litterbox or her pen. She is also very skiddish when eating leaves outside her hutch. Like If I put her dinner leaves out in her pen, she bolts when i get near her. When I have it in the pen, she can be eating out of the bowl while I try put it in the spot it needs to be and does not even care if I pet or nudge her.

In short, I think rabbits like to have a spot to feel safe in and stays there most of the time and runs there when something happens they do not like. Like hearing an unknown noise or song. Nom nom song still drives Peony nuts.

Very normal. We have several NIC cages for our rabbits, but 60% of the day they are out of the cages. They just hang out, hide under tables and chairs when frightened(very rarely), and sometimes get into mischief. They get to do their own thing and we are fine with that. As long as they don’t destroy things(we bunny proofed), of course. But they rarely do. New environments can be scary for new pets. Just give her some time and DO NOT force her to go places she doesn’t want to go, since she is still getting used to the room.  This is our bunny room. 

Most of the time my Henry will follow us from room to room, but he has ‘days’ when he doesn’t. Why? Who knows? We don’t even give it a second thought now. I spose like us, he has days of socializing, wanting to be in the thick of it and days he can’t be bothered with us (I took it that we bored him? Lol!). Like everyone else – I wouldn’t worry. My Henry is moodier than me, and I just put it down to ‘his’ personality. Cheers DebbieP.