When do I use Abbasta (do I have the right spelling?) and when do I use Abbastanza? Both mean enough don't they?

Do you mean "basta" and "abbastanza?"

Sorry yes basta. I was going from memory and really should have looked it up. So what is the difference?

Basta is from bastare, I believe, as in "Basta una?" Or "Due non bastano." Used as an expletive, it menas that's enough!
Abbastanza describes a sufficiency of something. "Come va?" "Abbastanza bene." "Quanto avevi?" "Abbastanza."

Quite exact Judith!
Moreover from basta you can say "bastava" "basterà"... I mean you can use it in different tenses. And use it in singular or plural as you said.
Abbastanza means "quite"/"fairly" when used as in "abbastanza bene" or "enough" as in "non ho dormito abbastanza" I haven't slept enough ( )

I rarely answer these queries because with such cultivated native tongues my answers may fall short, but your encouragement, Giulia, gives me a little more courage to do so.