We have 5 cats and 3 covered litter pans.  None of the cats came from places
where covered pans were used.  They immediately began using the covered pans
we showed them.  No problem.

If you're switching from open to closed, it might help if you put used litter
into the new closed box the first time.  It should make the association
virtually automatic.

Depends on the cat.  Some cats take to it right away and have no
problems.

On the other hand one of my cats would not use it.   It had one
of these "plastic" doors that she could just walk through, she never
grasped how to use it.   Ended up geting rid of that litter box
she didn't like the door or the cover.   No matter what
box I get she will not tolerate having it covered.

I also have at least two litter boxes for each cat.

I changed my cat from open to closed and she went right in.  I put it in the
same spot but didn't use the old litter.  she went right in and didn't seem
to notice much change.

Beth

Our cats did not like the change, either.  We had to leave the lid off of
it for a while.  Once they started using the new litter box, we replaced
the lid.