How do I check to see if my van is running off of the battery instead of the alternator? It seems like my cable wires are lose down at the bottom

Your car should always run off of the alternator once it's started. If the wires are loose your battery just won't charge back up properly. You draw off the battery when you start the vehicle but the alternator can't replace that charge as well if cables are dirty or loose. Your system should run somewhere around 13.5 to 14.2 volts if the alternator is working properly. If when you turn on the headlights that voltage drops below that then the alternator is weak.

Have you been having trouble starting it? A real easy way would be to attach a multimeter,( DC voltmeter) and check voltage before and after engine is running. Should get 12-12.5 volts not running, and 12.8- 14.5 roughly when running, depending on how much charge battery needs at the time, which is regulated in the alternator.
If battery is lower than 12 volts, you may want to have it tested to determine it's condition.

I think so thank you so much