Yes mine dose
yes
Yes and so do mice and other vermin
No
Mice can get anywhere they want to go, they have no spine so can squeeze anywhere. climb anything, up pipes, so the answer is Yes.
Why not? They have legs, right?
because red tree mice climb red trees and heather mice climb heathers underwear.
Some mice may be attracted to cedar wood due to its scent, but it is not a guaranteed preference for all mice.
They might try, unless the steps are to high. don't let them climb down the stairs though, because they could fall and break their bones. I also wouldn't leave them unsupervised near stairs, even if they're trained.
yes they are pretty good climbers
Mice usually try to run away from you, but rats do climb all over you if you font move too much. It does depend on the specific mouse or rat though.
Yes, Rats can climb along a rope. They do it all the time.
wood mice have the color of brown like wood.