Good evening, all. I'm working on my first saber and of course my ideas have outreached my knowledge. The plan is a retrosaber with a small internal battery (NiMH or Li-ion), a much larger belt-mounted battery (Li-ion probably 32650), and a connector for a wall outlet (probably through USB).
I know that the easy way is to run three separate power circuits and add a selector switch. That would allow all three modes of operation without any fear of damaging the batteries, but I'd like a more elegant solution. Ideally, the internal battery would charge from the external battery when connected (even if the led is on) and both batteries would charge from the wall when connected (even if the led is on). I realize that might not work, so here are some questions to see how close I can get:

Question 1: I know it is recommended to not charge the internal Li-ion while the led is on (to protect the lifespan of the battery), but what if the battery and the led are on two parallel circuits separated by a DPDT switch? Or would it work better with NiMH?

Question 2: Is it practical to charge one battery from another, or should I just scrap that and charge them both from the wall only? I assume one Li-ion can charge another if the voltage is the same and there's a diode to make sure the power flows the right way, but I don't have enough confidence to try it.

Question 3: If I plug it into the wall and use it as a lamp, do I need to worry about burning out the led?