I would go to
http://www.phatg20.net to download your FSM (Factory Service Manual). Then google for some software to decompress the .rar file that you download.
I think you have several non-related issues going on... something electrical (alarm issues) and something in your cooling system. You will need to get the cooling isuse fixed ASAP. These engines won't take many overheats before they're toast. Even one good overheat can do substantial damage.
What is the service history on the vehicle? In the U.S. every Infiniti dealer has access to the records by VIN, so you might check with one to get a copy. I wonder if your car has some prior repaired damage from an accident... not that an undamaged car can't have gremlins like this, but it's far more likely in one that has been rebuilt.
Welcome to NICO!
Heath