I think that the use of PM in boinc's projects is "intricate". I have to logon to project's website, go to "My Account" and, in private messages, click "Inbox" or "View".
Is it possible, if i have received a PM, a simple pop-up when i logon?
Or, better, a message in Boinc Manager: "You have a Pm"??

I believe that already happens as a 'notice' - and unless you have notice reminders turned off, that means a balloon pop-up too. But BOINC isn't in constant communication with project servers - most projects only check for new notices once every 24 hours.

If you want to be notified more quickly than that, you can choose 'notify immediately by email' from the project community preferences, and then you get the full text of the PM in your mailbox (though you have to log in to your project account to reply)

I believe that already happens as a 'notice' - and unless you have notice reminders turned off, that means a balloon pop-up too.

I have never seen this pop-up.
It's only for PM from Admins or also for PM from other volunteers??

If I'm right, it's for PMs, period. Admins don't get any special treatment there. Once you've viewed the PM via the website - so it's no longer 'unread' - then the notice is cancelled.