No, if you ride till its at 1/2 charge, it can sit there for a very long time with no damage.
You can charge and discharge from the same cable, but then if you only have one cable, you would have to unplug it from the controller to plug it into the charger.
By having two cables, it makes its easier. The charging cable is typically using 5A, so the wires can be light, maybe 14ga. I recommend a female XT60 for the charge cable.
For discharge, the bike can often use peaks of 30A, so I'd use a thicker wire, maybe 10ga/12ga. A female XT90 connector is a good choice on that cable.