I am American and speak English, and I always have heard "aunt and uncle" and have never heard "uncle and aunt." In Russian, do they say it in the opposite order: as "дядя и тётя"?
I don’t think it has anything to do with the fact that an uncle is a man. It’s just a matter of set collocations.
In support of this - whatever a collocation is - these exercises include мать и отец = "mother and father".
In English, I think that it's "aunt and uncle" because it flows better, sound-wise: the simple "t" in "aunt" flows easily into the "a" in "and". It's a much more complicated set of sounds to say "uncle and aunt". The same with "Mom and Dad", but less evident. "m" flows onto "a" more easily than "d" onto "a".
"mother and father" is accepted for мать и отец. If "uncle and aunt" isn't accepted, I'd report it.
Mind you, that these words are also used (especially by children) toward any unknown man or woman
No, without context it is hardly possible to decide between singular and plural.
It sounded right to me, but I also believe that "дядя" is pronounced more like "дяда"
No, it's not. What you suggest would give the second syllable a hard д not a soft д as the я causes. It is usually said quite quickly though.
This sentence is good practice for palatized Д and Τ. Repeat to the end of days.