The "correct solutions" to different questions have different rules of using "an/a". Sometimes it is used, and sometimes not, I cannot tell when to use it.
it is indeed so. we do not have articles in Ukrainian and the translation of english ones into Ukrainian is sometimes tricky. The sentence я не люблю подорожувати з дядьком mainly means "I don't like to travel with [my] uncle" because if we say дядько or тітка (uncle or aunt), we simply don't add any other specifications in colloquial Ukrainian. So the variant with the closest meaning to Ukrainian sentence will be I don't like to travel with my uncle. But this is the study course and the main principle here is not the translation of the sense but the word-to-word equivalent sentences because they confuse less and take less time to design.
Returning to the word дядько, it can also mean "some stranger" or "a middle-aged man that is familiar to me (I am much younger than he is)"
Wow that last point is interesting - does it work the same with тітка (she is some random woman who I know, but who is a lot older than me)?
It's usually a random woman/man who you don't know. And kids (and a lot of adults) call their parents' friends дядько [name]/тітка[name]
I don't know if it's still the same for children today, but when I was growing up in 60s/70s England we would call our friends' parents or other adult neighbours etc Aunt [forename] and Uncle [forename].