Battery light on

Started truck w no problems and the battery light is on. Can you tell me why? A week ago I had one incident when starting the car hesitated for a minute, then turned over, but has been fine since then. I am afraid to turn the truck off. I do not know if this is relevant or not but every six months or so one of my headlights goes out. They tend to go back and forth between the driver and passenger side. Do you think maybe I should check/replace fuses? Thank you in advance for any help you can give. I am a single mom trying to fix things myself. Cars are a little trickier for me.

Thank you,
Andria