Azeri conjunctions (and, or, but)?

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To all Azerbaijani-fluent members, can anyone help me with conjunctions? I'm having trouble finding info on the correct use of these...

I've seen 4 words for "or" - ya, və ya, yoxsa, yaxud. I assume they're not all interchangeable. Is one "and/or" and one "either/or?" How are they used?

I know amma means "but," but azerdict.com lists several other translations - ancaq, lakin, yalnız, and more. What's the difference?

Also, what about the conjunctions in these sentences:

Both Sarah and I live in Baku.

You can have either rice or potatoes.

Neither Vuqar nor his friend were at the party.

The balloon is not green but (rather) blue.