One thing that may help you is researching starbases and auxiliary government/enforced loyalty/whatever it was called for the advent. If you have a starbase with that on your key planets you can make sure you keep them even if they are being bombed by Novas.
The Advent superweapon can be countered by just placing a culture center on every planet.
Other than that the problem lies with the AIs, mainly the TEC loyalist AI. As they have forgotten how to build large fleets and nothign better to do they ride the "lets spam superweapons" horse. There is currently a limit of four weapons per player, but that is anything but a viable final solution, more a patch until the AI has been fixed.
If you want to gain some experience, go online with ICO and search for a bunch of guys for a team game. There should always be some nice people around who are not going for the "stomp the enemy in 30 minutes" games.
