Rick,
Complete answers to those questions would take a book. It is great that you're thinking of this stuff, though. Here are some thoughts to get you started at least:
1. Yes, you need to look for them. You can also disable or remove the stops on most rails.
2. A screw or two can hold it in place, there's a million possibilities here.
3. You must use one 50 A connector, and I think it's only legal to use one, not a second one! Ask FIRST next year, but I think you can get away with one only.
4. Correct. I doubt the judges would allow fiber optics or a similar scheme. The visibility rule is also to help you - if there's something wrong, the field techs can help diagnose it quickly with the lights.
5. Flat is OK. You can solder too, but good luck if something goes wrong. Instead, use hot-melt glue OR silicone sealer to hold everything tight - holds but removable. Also applies to PWM and other cables.
6. I don't think that was interference, I have seen it on many robots. Really, the PWM frequencies are kinda low and not likely to see much crosstalk. If you really must shield the wires, just but round shielded 3-conductor wire. Remember to ground the shield at one end only, or you'll get ground loops.
7. Yes, look at
Figure 2 but that's not going to help you much. One possibility would be to make up a connector body and wire everything over to a different kind of connector, say screw terminals. (Remember, all the Red and Black pins are the same, only the White pins matter!). Or, see #5 above.
The biggest problem with what you propose is how to make and break all those connections (to the sensors, motors, etc) reliably and quickly. One expensive but good solution would be
Circular MIL Connectors (look on the second page). Really high currents (check the contact rating) can use two or more pins in parallel. Clearly solvable, but you need to think about it.
Another possibility is to make a fold-out panel, so you can access it easily when you have to, but it's tucked in at competition. Eliminates a lot of problems with connecting things, too, you just need to allow for the wires to flex at the "hinge"
Good luck,
Don