re:ABS
if the ignition was left on for the first tow the car may have thought that the front wheels (or brakes) had 'locked up' causing an abs fault. this would not damage anything, just needs to be reset.............
BUT-
if the first tow job was a hack, the front abs speed sensors may have been yanked / killed by a chain or hook.

hope it all turns out ok for ya.

PS, I'm not sure I buy the 'just a bad battery' claim, sounds like worn brushes on the regulator.