Why does the pronunciation of "bainne" sound like "bahn-ye?" Is that always how "ne" sounds?
The “y” sound is a reflection of the “slender” N. The Ns are slender in bainne because they’re adjacent to “slender” vowels — E and I are the “slender” vowels in Irish.
Is the "y" a distinct sound (like ñ in Spanish), or does it have to do with where the "n" sound sits in the mouth? (Sorry if I'm articulating poorly; I've only ever had one uni linguistics course several years ago.) Is it a regional dialect thing?
In phonetic terms, it represents palatalization. The “hard” and “soft” contrasts of consonants in Russian and Polish represent the closest analogue, with “soft” corresponding to “slender”. The Spanish ñ, /ɲ/, could be viewed as an Irish slender N with an overemphasized “y” sound; the Irish “y” sound is an offglide. All of the dialects have a slender N; some of them have two varieties.
How do you decipher by listening if child is plural or not? They sound the same to me.
I don't know the plural form of 'child' yet, but the article in front of it will change. 'an' is singular, 'na' is plural.