I'd like to install a second version of Zenphoto with separate database and all on the same server. Will everything work just fine by changing the name of the folder I upload everything to? Example: instead of uploading to mysite.com/zenphoto can I load it to mysite.com/newzenphoto?
Then I'd have it create a new database with a different name also.
Should this work O.K.?

What you describe should work. You can also allow two copies of zenphoto to share a database if you give each a different table prefix in setup.

I have 3 copies on my server, and everything is running smoothly.