No. The plural is bataichean.
Bhàta is the lenited form of bàta. To be honest the difference is that bhàta is easier to say in some situations than bàta is. So you basically know when to use lenition as if it's hard to say and lenition makes it easier, then you use lenition.
In Gaelic the numbers one and two both trigger lenition. I am not 100% sure of the linguistic reason for this, but both those numbers come feom a defunct counting system Gaelic no longer uses. I imagine that's why.
That is not the logic. It was, 1000s of years ago. The sound changes occurred after words that ended in a vowel because it was easier to say, but since aon no longer ends in a vowel, the logic no longer applies. You just have to learn which words cause lenition, unless you happen to know which words ended in a vowel 1000s of years ago.
You use the lenited singular 'bhàta' after the numbers 1 and 2, the unlenited plural 'bàtaichean' after 3, 4 &c. There are other rules like you lenite in the definite genitive eg 'seòl a' bhàta' (the boat's sail) but you'll have to learn these gradually as you go long. Of course they are general rules, not applying to 'bàta' alone.