To disable the startup beep is easy: just edit the gdm3 conf file or probably installing the sound themes disables it automatically.
For the shutdown beep then I don't know (nor how to make GNOME work with a login/logout sound; actually I think there's a thread on this in Debian forum but it involves some hacks, IIRC).
The "Login Screen" app doesn't work in gdm3 2.30. I've wrote to Clem about that. I suggest to simply remove the desktop file for it so people won't complain of it not working. If there's time for it, a simple app could be made for that or a setting added to Mint's desktop manager as to enable auto-login it's just a matter of editing a file (for the next respin at least it would be a good addition as, for now, gdm3 3.0 also uses /etc/gdm3/daemon.conf for that).
* edit- actually automatic login can be set in the user account settings in GNOME 3 (didn't check if it works, though).