backfiring on its own is not dangerous. it can cause stuff to blow off (intake ducting etc) but if it's bad enough to cause damage, your engine won't run.
Backfiring is dangerous, and yes it can blow off the induction, carburetor, etc...it can also set fire to the inlet filter, cowling interior, etc. It can cause damage to intake components, cause induction leaks, and consequently cause uneven lean mixtures which can result in engine damage or engine failure.
An afterfire makes a bang out the exhaust. A backfire makes a bang out the intake. After excess priming, it can set a fire that you're not going to suck back into the engine.
If you've had an engine fire, you certainly don't need to go flying. You need to have a qualified mechanic pull the cowl and perform an inspection. This is common sense. I say this as a pilot, mechanic, inspector, and instructor.
Your battery was dead. Your aircraft was unairworthy. The battery shouldn't be charged in the aircraft; you'll find that in both the aircraft flight manual, and in the maintenance manual. Depleted batteries being charged create heat, and explosive gasses. You don't know why the battery is dead, and the fact that it's dead could be a short, could be a bad battery, could mean you have other electrical faults. If you have faults in the airplane, correct them, learn why they exist, before you fly.