My 4wd does that occasionally as well when the jeep is moving. It's not too loud of a bang but its audible. I dont really worry about it, most of the part time vehicles i've owned have done the same thing when they're in motion. Just bring the speed down a bit and let off the gas and it should help.
About the 4wd light, there is a little hydraulic sensor thats screwed into the transfer case. My TJ had the same problem when i bought it and i ended up bringing it back cause it was still under warranty and they changed out that sensor. I think it's like a 25 dollar part, and the light works perfectly now. I'd imagine its pretty easy to change yourself, the mechanic showed me the old one and it was threaded and just looked like it screwed into the t-case somewhere. I'd imagine once you find it you just unplug the harness that connects to it, removed it with a socket wrench, and then put a new one in and plug in the harness again.