Hi and welcome, I'll take a stab at this
1) Yes, you can pedal and it's called "pedaling" heh. Biggest problem is there is something always turning in the motor with all it's attending drag. Yet it beats walking home if you have to
Proper clutch adjustment can help by not dragging.
2) Yep, I'd say just get a bigger-than-stock rear gear. Stock gear in my kit was a 41. Before the thing ever rolled I had a 56 on it due to hills and a 28" tire. A good hill climbing gear for stock motors is like a 48, maybe a 50. You can't have speed and hillclimbing in the same bike without a shift kit.
3) The shift kit From Sick Bike Parts moves the power from the left of the bike to the right side via a jack shaft and with other components drive off your bike rear gears. You lose the front derailleur in the swap. 4 strokes are not geared in general. There are way to add the shifter or a Constant Velocity Transmission like the NuVinci set-up.
5) There are some, somewhere but I don't know where. A lot of times find the right sub-forum and ask. Most will be willing to help. Many times the bikes are the same just under a different name.
6). Like a lot of the parts that come with the kits they are junk and stretch a good bit. I've shortened mine twice since the initial set-up. A US made chain can be found in size #41 from Farmer's Supply for $10 for 10 feet. Get a couple of spare Master links while your at it.
Hope this helps