Sleeping/Pooing

Hi
My 5 - 6 month old spayed female rabbit called Poppy poo's and wee's in one corner which is good.

She often lays down and maybe sleeps in the corner where she poo's even though we have bought her a bed.

How do I stop her lying there because she has recently been getting lots of poo stuck around her bum which isnt nice for her or me

What shall I do?

How much room does she have as her living quarters ?

Do you provide her with a litter tray ?

She had the bottom floor of the daisy cottage and we have removed the stairs so she can have more room.

Also living upstairs which is blocked off to her is my sisters rabbit loppy and he is a good rabbit, but when you try and pick him up he scrables and runs about but eventually when he is out he has a good time. How can i get/lift him out easier?