I listened to it 8 times and i hear the same thing

The same here... I don't think it's the right pronunciation.

because om=human, bărbat=man. but here om is used often for bărbat

I think they're pretty much synonymous.

they are synonymous, yes

bărbatul is "the man"; bărbat is "man".

eu is "I". You wouldn't say "I man" or "I the man".

Its not, you can use both

That's the official answer, but there is more than one word for "or". If you had a multiple choice question, you needed to select all of the correct answers, not just one of them.

It's one word for "or".

https://forum.duolingo.com/comment/19115519/The-woman-does-not-drink-the-tea-or-the-water

https://forum.duolingo.com/comment/19134790/You-eat-or-you-drink

https://forum.duolingo.com/comment/19419062/Romanian-cake-or-English-cake

https://hinative.com/en-US/questions/3098892

https://hinative.com/en-US/questions/3293756