Singing songs in foreign languages is one of the best ways to learn those languages.

I am a language teacher (I teach Punjabi), and I make my students learn songs. I have sung songs in Spanish, Hindi, Urdu, Persian, Arabic, Low German, High German, Norwegian, Yiddish, Hebrew, French, and got the "feel" for some other languages from ditties. There's absolutely no reason not to try it. It's not as if you're trying to become the native voice of the Irish people or something.

The quasi-phonetic Anglophone renderings of pronunciation can be really useless at times, but also very helpful if one uses them as a sort of Rosetta Stone, for clues that otherwise are not being explained well.

However, the OP asked for a more sophisticated list of pronunciation rules. These are a bitch for Irish. Even if one learns the rules, there are many exceptions, which is why the Rosetta Stone of (multiple) "phonetic" renderings helps to clarify. After that, one tries imitation, which is what language learning is.

Gotta crawl before you can walk; sing before you can talk.