moderator getting email notifications
 

Do you think it will be possible to lets my particular moderator getting email notifications when someone posts new photos in the gallery? It's very confusing and time consuming to look through all the photos posted for new ones, it's going to be impossible to keep track of them

Only admins get email notification of new photos if you set that setting to yes in admin. Your not going to get mods an email unless you write some sort of code modification to do that.

So, can I set administrator privileges only for the gallery?

The email is ONLY sent to the global email account on file in global options in admin. it does not query any user status and send out emails