Depends on the year of the vehicle, but if it's slightly modern - absolutely. A disconnected or faulty speed sensor will not allow it shift out of 1st or 2nd gear. The cars computer has to know how fast it's traveling to determine shift points I think. I'm not familiar with your particular car, but there could be other sensors that have an effect on shifting as well.
No, the alarm will not affect the trans.
YesYes
The starter has failed.
No.
A failed starter is a likely cause.
The abs computer detects a malfunction and sets a code.
Engine, Transmission, Body, can all prevent starting in different ways.
The blower motor is failing and will need replaced.
Short in the wiring or the lamp holder for the tail light is corroded.
You either didn't swap the tire sensors to your new rims, or you damaged a sensor.
The body computer is on the back side of the dash fuse box. It is one of the computers in charge of the theft alarm. That can cause a no start.
pee on it