Jesse - you've got a tons of questions there! If your questions remain unanswered, try assigning numbers to ease the separation, and its usually easier if you add more returns to make things easier to read.
You may very well want to run a motor at much higher than specified voltages for your car. For the same power, the higher voltage offers less I^2*R losses in the wiring so you may be able to gain efficiency. Especially true if you use a PWM motor drive to limit the current in the motor so you don't end up delievering (and extracting) more power than the motor is designed to handle, although cooling could prevent that and would likely be advisable to minimize the thermal resistance rise in the windings.
Lead acid batts have less energy density than NiMH or Li but do have massive cost benefits. How you array the batts and cells for higher voltages you can likely find some system that will allow the system to be arranged as two parallel stacks or some other logical grouping depending on how many are determined to be used. If you're using 50lb car batteries I couldn't imagine you'd use too many of them...
Regardless, it can be setup as isolated systems (one panel charges one battery) and those isolated systems (say 3 of them) can then be wired in series to produce the 36V you need. Charging could be tricky because of isolation - it may very easily not be as simple as hooking up 3 chargers with one on each battery because sometimes the negative lead is tied to the neutral (ground) of the AC outlet. So then you'd need isolation switches to allow the batteries to be isolated from each other and break the series wiring to prevent a charger from shorting out. You can find 36V chargers but the rarity means big money.
You may also want to oversize the panels and use a charging regulator to accommodate the sunlight angles and respective intensity. It would be better than having a charging condition under ideal conditions and nothing other times.
Seeing as how the standard PMDC motor runs at peak efficiency at roughly 1/2 peak unloaded RPM, I'd be looking at motor graphs and pick that item as soon as the rough chassis is built and a bicycle chain drive or whatever is chosen. A gear reduction drive like on wheel chair motors may help get the RPMs inline for large bicycle tires and so on, or even some of the battlebot motors that surfaced have high efficiency and power density.
Sounds like a fun project with tons of variables to work out and multiple ways to accomplish the goal. Good luck.