what' cha havin'?

Hiya Lynn
I suppose it would be the contraction of 'what are you having ?' usually meaning 'what would you like to drink or eat ?'.
Not 100% sure, depending also on the context, but that would be my take...
Waïti.

It means: what are you having for lunch or dinner (or whatever you are eating at that moment).

Similarly there's ''what'cha doin' '' = what are you doing?

watcha makin' = what are you making?

where didja go = where did you go?

All in speech only though, don't go writing like this unless you are deliberately creating this type of dialogue.

I should have added, Brits hate this kind of abbreviation...right Nona?

Well we nearly all say them, but don't write these ones...