No, it isn't normal or idiomatic to use "meet" in any of the situations you describe, including the zoo. It can be done, but it would be unusual, and it would typically only be used by a native speakers in order to create an unusual emphasis, comparison with human encounters, or irony. Part of the problem is that "meet" doesn't just mean "encounter" or "meet with," it implies being introduced to a person, having some social interaction with them, and learning to recognize their face so you will know them the next time you see them. There is an implication that the familiarization, future recognition of the individual, and social interaction are mutual, not one way. So, for example, it would be idiomatic to say:
She told me I could use her bathroom, and while I was there I met her cat, an old tom who looked at me suspiciously but clearly didn't want to be stroked.
It would not be normal to say:
I sat down in the restaurant and met the waitress.
You don't really meet the waitress. She won't remember you next time, and you don't introduce yourselves or interact socially except in a very limited way. There would have to be some other reason to use "meet:"
I sat down in the restaurant and met the waitress. Her uniform said Amy on it. I told her I was from out of town and asked if she knew a good place to stay that was cheap. Yes, Johny, that was your grandmother.
I think you can go to the zoo to "meet" animals, ...
No, not really. This lacks almost all the necessary elements: familiarization, future recognition of the individual, social interaction, and mutuality.
Someone wants to see a wild deer and perhaps take some photographs of it. When you know a road around which deer are seen very often,
... you would idiomatically say...
You can see deer on that road.
Sometimes there are deer on that road.
You might run into (encounter, meet up with, cross paths with ...) a deer on that road.
Once in a while you get deer on that road.