I don't have any solutions for your car troubles, but I do have some advice to offer. Driving a car for three miles and shutting it down is the worst possible thing for it. The engine and all it's fluids have barely warmed up. In your situation, you should be changing the oil more frequently then the recommended interval, I'd say every 2000 miles or so in your case. Also, three miles is probably not far enough to re-charge the battery to the level just before you started it...which is probably why your battery is not lasting as long as it should. The ABS and ASR lights are probably coming on due to low voltage caused by your very short commutes.
Very short drives will cause almost all the mechanical systems in your car to deteriorate faster than normal. Also, the exhaust system will tend to rust out sooner as it accumulates moisture that would otherwise be vaporized with a fully warmed engine.
If at all possible, try to take your car for a good long drive at least once a week. The engine needs to get to operating temperature and stay there for at least a half hour. Also, try to use a good quality fuel, if not every tank full, then every other or every third. Something with detergents to keep the fuel system clean, ie. Chevron with Techron.
I think you will find that your car will run better if you drive it more. Best of luck.