I can't really answer all your questions but here goes. I own everything that you have listed except the power supply. And it all works very well with an AXE or a Blade CP Pro. The charger takes about 1 hour or a little more to charge that battery. I have an old 12volt power supply from Radio Shack rated at 2.5 amps, and it works great. You should get about 10 minute flight time with that battery.

There are chargers that will work with both AC power and DC power. I think they start around $100.00. My friend has one but I can't remember the manufacturer. I can find out for you though. I have flown with him and it is a good charger (no balancer though).

I am kind of new to lipo's though, so I would also be interested to what anybody can add to this.