Low battery light means the battery isn't charging, doesn't it? So, although you managed to get the car back home, there's not enough in the battery to do anything else.
Try charging the battery, for starters. Then, if you can get it going, check the voltage on the battery - should be around 14.4 volts. If lower - say 12volts or so, the chance is that the alternator (or charging wiring posssibly) is knackered.
Checking and changing the alternator isn't too difficult but the fact that you have asked the questions you did, suggest the task may be best done by a techie.
As for the oil lamp , that could be low oil - check the dipstick - or any one of a number of things.
XXX
April 2016
howtomendit.com for free repair help, information and advice.
