I've been casually zapping a couple of pets hoping for neela but then it occurred to me ask: is that even possible?

I have never gotten one by zapping, I ended up puichasing mine direct. The FAQ doesn't mention it as a possible, but it doesn't exclude it either. So maybe, but extremely rare?

It’s a pet that’s exclusive the the Cash Shop only. Just like Angelic. You’ll never get that colour zap.

You also can’t zap for a Bhakaru either

You absolutely can zap for bhakoru. I've gotten a bhakoru zap multiple times. :)

Whhhat!!?! I know in the past the zapper never gave them. Unless they changed it

Maybe they did? I got a glade bhakoru zap some months back - I remember because I was conflicted on whether to keep zapping or not. And I just got a basic color bhakoru zap in the last couple of weeks.