And why рік instead of рик ? Any trick or advice on when to use і instead of и ?
Well, it’s pronounced differently. «І» is a higher vowel than «и».
«І» is often found in closed syllables (i.e. syllables ending in a consonant, not just in a vowel), where it can alternate with «о» and «е» in open syllables. So, «рік» becomes «роки» in plural. «И» doesn’t usually alternate with «о».
My audio exercises are not picking up my pronunciation of the numbers at all. I even have my roommate who speaks Russian listen to me, and she says I am saying it exactly how the example says. Is there a known issue with the audio files??
Because it a rule for masculine noun. It depends on the word's ending. So the word "рік" has masculine ending. Look up the youtube channel Olga Reznikova, she does good and helpful Ukrainian lessons. Hope this helps.