I tried to upload ZIP files, but appear error - not allowed format. Why this happen? May be i didn't activate some plugin or didn't something in setting?
Anybody knows?

That possibly means that your server cannot expand zip files. zip handling is a PHP extension that must be installed and is normally part of a default installation. Not all servers are the same sadly.

Look at the php information button on the Zenphoto overview page and if there is no "zip" extension listed you might need to contact your host about that.

I checked in overview. All zip extension are normal. I tried upload zip directly by provider cpanel. It normally uploaded. But i can't see uploaded zip file in overview panel of my zenphoto gallery. Why?

As I sad your server requires the PHP zip extension to be able to process zip files. If it doesn't it doesn't work.

Also perhaps a misunderstanding:
Uploading zip files is meant to be used to upload several images that are zipped. The zip file then will be extracted so you get the images. That will of course only work if you upload via the Zenphoto backend. Which you can't as your server doesn't support it.

Uploading via FTP of course will also not work since Zenphoto is not involved in the upload.

Directly upload a zip file so the zip file appears in the gallery is not possible for above reasons.