I know the Neela is one that won't happen from the zapper but what others are also not possible via zapping?

Bumbus, I believe. You can only get them from the blue building.

i'm pretty sure the zapper also won't give you a bhakoru, but i can't find an actual list (unzappable colors are listed in the faq, but not unzappable species)

The three already mentioned make sense-- I'd assume that it can zap into any species that can be created "normally", not through a quest, the CS shop, or other special means. This could also exclude Zentu (made at the bathhouse) and Aeanoids (made at the gardens), but I'm not 100% sure as it's been an incredibly long time since I've used the zapper for anything.

I'd assume that if you can create a pet species normally, it can be a zapper result.

Can confirm the zapper does give Aeonoids, don’t know about Zentus.

The zapper can give bhakorus, and I’m pretty sure I’ve gotten bumbus too. I’ve heard it can give neela, but it’s never happened to me personally.

It won't zap the Angel or Hydrus colour.

The zapper won't give you Bumbus (Blue Buliding exclusive) Neela (Cash Shop only) and Bhakoru (created in the desert). I'm not sure about the Zentu.

The zapper will give neelas. Me and a friend have gotten neela zaps in the past, unless it was changed recently.

I got a bumbus zap on my pet Rumi and I left it ever since because I'm still unsure what I'd like her to be lol

I've gotten neela before, but it was ages ago; Probably when they were first released. It might have been changed since then.