Make sure your ground strap from the frame to the starter is good and clean at the ends where it connects. Take the bolts off and clean them. Clean the flat surfaces of the starter and the frame where the straps attach. It sure sounds like your starter is trying to find ground and getting it through the throttle and choke cables, at least partially. The dragging starter is another sign of a poor circuit.
I would also clean the battery cable connector where it mounts to the starter, and check both connectors on the posts of the battery.
