It's always the 'i' in 'it' or an "ee" sound for South Wales. North Wales has a slightly different pronunciation, sort of like the 'e' in 'roses' ('ɨ' in phonetic notation), which might be what you're hearing. North Wales is the same as Polish 'y' and Russian 'ы'.
'y' is the same as Welsh 'u' in final syllables; everywhere else it's how most Welsh accents say the English 'u' in 'cup'. If you don't have a Welsh accent, your "cup" sound is probably similar, but it's the same as the 'o' in 'today' or the 'ai' in 'mountain'. Exceptions: y, ym, yn, yr (which have the 'cup' sound). The technical name for this sound is 'schwa' (ə), and it's very common in English, so don't worry too much about it!
Both parts of Wales say the letter 'i' like the "i" in "it" or "ee" though.
It's a difficult sound unless you happen to speak Greenlandic, Zulu, Navajo or some other language that includes the sound. The first stage is understanding how to make the sound and then the second is just practice, practice, practice. It helps if you listen to Welsh a lot and copy. Pob hwyl / All the best!
That figures as Welsh held a lifetime fascination for Tolkein and was a big influence on his language Sindarin: https://en.wikipedia.org/wiki/Sindarin#External_history.
The Irish "r" is more like the tapped "r" in pero (also how a lot of Americans pronounce the "d" in "madder" and the "t" in "butter").
Rolling the "r" t can seem tricky to English speakers at first, but it does come naturally if you keep at it. Even if you use a slightly different pronunciation, it's unlikely to affect comprehension.