Which one is correct "have you had a breakfast" or "did you have a breakfast"? And should I use the ‘a’ s, is it necessary to use it?
Neither is correct!
The usual question is either:
Have you had breakfast (yet)?
Did you have breakfast - usually, but not necessarily, followed by a time reference - this morning?
However, one uses the indefinite article before an adjective preceding breakfast
Did you have a good/hearty/substantial breakfast this morning?
Have you had a good breakfast in preparation for a hard day's work.