How Do I keep these faggots out of my garden shed?

Mice have been living in my insulation in the walls and roof. I believed they couldn't get in at the bottom. Can they climb wooden walls?

I have a wooden floor and have insulation in it too.

I guess I need wire mesh. But I can't get under my shed. So do I need to lay it down under the floor then put insulation back on top then floor boards?

Should I dig a trench or will these faggots burrow underneath it.

Do I need to protect the roof joins also?