Any question answered...

Mice and other rodents normally access compost bins by tunnelling under
and up into the fill.

Avoid putting any cooked food into the compost,
and,
sort out a solid base.

I recycled some paving slabs from a neighbour,
making a rectangle an inch or so bigger on both dimensions
than our two compost bins.
I then made up a frame from reclaimed wood from pallets which ensured the paving slabs could not slide apart.

A couple of shovels full of 'mud' from the bottom of another compost bin,
with a plentiful supply of compost worms, (which are not your commonly encountered earthworms),
and its worked fine and rodent - free for the last 4 years.

I was planning to put it at the end of the garden, as far away from the flat as possible... there is about a 2m x 2.5m area that is solid concrete, so I guess based on what you have said, it should be OK?