My reverse light stays on

Test the main battery cables , voltage drop testing .
Starter Voltage Drop

Check to make sure linkage is tight.

My truck did the same thing, but what happened was, the smaller second wire on the starter broke. Once i fixed it the starter would shut off like normal.

E brake ,please explain if this has an electric auto handbrake like a renault megane or is it all manual with a pedal on the side or a proper handbrake in the middle

You kind of answered your own Question. If the shifter is a floor shifter and not on the column I would check the linkage there. Do you have reverse lights? And after it starts does it go into gear or is it a dead stick? I would also check to see if the shift cable on the trans is moving with someone moving the shifter. It might be the cable or module on the brake pedal. Give more info after trying these and let me know.

considering its winter the best way is to put some thing in front of front tires and try to move forwards if you cant put it in 4 wheel mode and then try it. if you climb over then axles are engaged.

if it won't engage reverse the trans will need to be overhauled, the rev clutch has failed inside the trans.

This is the problem with faulty reverse light switch which is in the transmission, replace the switch it will the problem ...

Good luck....

Your car has pass lock I, this is an easy fix. Simply attempt to start the car. The theft light will come on and may flash. Leave the key on after you try to start it for about 10 mintues. IF indeed it is a passlock I issues it will relearn and start up after 10minutes. If at anytime the key is turned back off after the intial start, the process must be restarted. Pass lock allows fuel to make it to the injectors and then pulse enough to get engine RPM to around 800 and then shuts the off injectors not the fuel pump. Let me know how you make out.