I've had one since the fall of 2013. With the battery life, I'd ride up the mountain for about an hour, then down the mountain for another hour or so - this is with some stops along the way to loosen up the cramping muscles. The motor regenerates and partially recharges the battery on the downhill sections - you can program how much regen you want. The battery would be low at the end of the ride, and I'd be happily tired anyway.
Always rode with earplugs. You don't get the engine sound of a gas engine, however you get the whine of the electric motor and the drivetrain. It sounds like a remote controlled toy truck that you see some people playing with, but louder. Overall though you could definately play with it in public areas without much complaint. More likely people would be fascinated.
To recharge, seem to remember that it was maybe about three or four hours to a full charge. Photovoltaic recharging (you said "solar") is not realistic as you wouldn't get the amps required unless you had a large photocell array. If you had a large photocell array, it would be mounted on the roof of your house, so you would just replug the charger into your house circuit anyway. If you wanted to recharge the battery in the field you would use a gas powered generator - but somehow doesn't that kind of defeat the purpose of having an electric trials bike??