"Eu nu am chitară, am vioară." Why are the indefinite articles dropped, why not "Eu nu am o chitară, am o vioară"?
I dunno. I see many of these and someone made a mistake. The indefinite articles can be dropped but mostly when they are in their plural forms, pretty much like in english. I gave this example in another thread:
Fata are un sandvici - The girl has a sandwich.
Fata are (niște) sandviciuri - The girl has (some) sandwiches.
It is pretty the same like in French: "Je suis ingénieur" + "Sunt inginer" vs "Je suis un ingénieur" + "Sunt un inginer". It is not wrong to use the indefinite article, but in casual speech sounds more natural without it. It is the same situation like the following one: "Sunt un băiat" vs "Eu sunt un băiat".
If you are still in doubt, don't hesitate to request additional help. Salutare!
Yes, when you use the "a fi" verb. With other verbs, it's tricky. "Am vioară" sounds unnatural to me. However if you ask a question like "Ai mâncat brânză?" you definitely drop it.
In simple sentences it sounds a bit weird.
"Ai vioară din lemn?"
"Da, am vioară din lemn."
For the second sentence: "Fata are sandvici cu cașcaval."
What I want to point out is that purely grammatically it is not wrong to omit the article, but it can sound weird in some contexts. Mulțumesc pentru observația ta! ;)