The rough/dying idle and no gas problem sound like exactly what was happening with my car a few weeks ago. In my case the Air Mass Meter was responsible for the car's inability to stay alive and the gas not working. If the alternator issue doesn't solve the problem, try the AMM. Unplug it BEFORE you start the car and see if it will at least run. If it will it'll run roughly and it'll smell like a gas station out the back because of an overly rich mixture, but it'll at least run. DON'T plug it back in or unplug it when the car is on!

If you have to replace the AMM be sure to check the Air Box Thermostat as well, as I was informed that its failure is usually what causes the AMM to fail prematurely due to it always sending in hot air. Another option is to just remove the hot air hose (the metal one under the car) from the exhaust or the air box itself, although this might cause problems at the emissions tests because it's supposed to be on in most states. Read some other threads about the benefits/downsides to always giving the engine colder air.

Hope that helps!

I'm really not too sure about the battery charge. Maybe it's a result of starting it too many times without being able to run it long enough to recharge??? Just an uneducated guess... :)

--
-jp ('83 245 DL, 210k, 4+OD, no A/C, piss yellow color - but hey, it's got a computer in it)