Gumart:
I would suggest you take your multimeter, and check charging voltage, which should be above 14 volts, with engine running and all accessories off. Leave the engine idling and come back in 10 minutes, and make sure the voltage regulator is doing its job and keeping the overvoltage at 14 or better.
Then shut it down, and place the ammeter into the battery circuit, and see what the current drain is for security system, etc. Take the battery amp/hour rating and divide by the drain rate; this will give you a rough clue to how long you should expect a new battery to last. I'm not sure what the factory spec would be, but I leave my '94 at the airport for weeks on end, and the electrics work fine.
I once installed a refurbished alternator that checked out fine on the bench, and installed, however as it warmed up, it lost voltage until the car ran on battery alone until there was insufficient electrical power to keep the ignition and accessories going. I died a number of freeway deaths until I figured that one out.