[FC Zach]

And it is driven by a plastic worm gear.

"1) Speed apparently isn't read by transmission speed or the rear wheels, cause I can spin them or lock them and the speedometer won't read."

If there are moments that it wont read when you are rolling then you have a defective gear. They are plastic and its not uncommon for this to happen, I have replaced two. Easy replacement, just one 6mm bolt.

Edit: that or a defective and/or loose cable.