I can't log in to my zenphoto site. Forgot the admin password and any other user names/passwords and have lost all records of them days (two, three years ago).

The only thing to do seems to be a reinstall from my reading today.

Will the photo album directories be safe and get incorporated in a new installation or I should copy them off somewhere?

Can it be reinstalled by running some currently existing within that installation on my host machine?

Or what do I do?

If you forgot your password/username you don't exactly need to reinstall. A reinstall will again require those credentials. But you need to access the MySQL database of your install directly to reset those. Please see here:
http://www.zenphoto.org/news/login-and-password-problems/#forgotten-admin-password
Ask your host how to access the database.

> Will the photo album directories be safe and get incorporated in a new installation or I should copy them off somewhere?

If you keep the root `albums` folder and the database used (although you seem not to have added any manual info) all should be save.
Please see here for installation and upgrade instructions:
http://www.zenphoto.org/news/installation-and-upgrading/