I was planning to nail 12.5mm plasterboard to the ceiling joists. The
joists
are 500mm apart. Do I need to put in "cross-pieces" between the joists?

For a shed, I wouldn't bother. Sounds like work. Of course, the ceiling is
more likely to crack without them, but do you care?

I was palnning to lay lengths of 35mm Celotex between the joists for
insulation. Is this OK?

That's a very good idea. Even better if you can lay them on top as well, to
eliminate cold bridging.

Christian.