The ABS relay that needs replacing. It is making the ABS pump run continuously, draining the battery and eventually kiiling it. This is a common problem for Subarus built mid to late 90's, and some models beyond.
The two issues could be connected, but they may not be. You may have an old battery that needs to be replaced, and this weak battery is causing additional trouble and throwing warning lights. If the battery is old, I would replace that. If not, then I would take the car in.
Here is additional information on the ABS light: http://repairpal.com/abs-warning-light