Hi, simple plasterboard question with luck:

When fixing plasterboard on wall studs and ceiling joists, is it OK to
screw the plasterboard on,

Yes that is ok


cover the joints with scrim tape, and skim,

Yes that is correct

or, is it better to fill all the board joints with bonding plaster
before taping and skimming?

No the adhesive Scrim we use now, will not adhere to a damp surface.

If you were using the old cotton Or jute scrim that was the way we did it

Kind regards
Edward