Sounds to me like you need to sort the electrical supply issues first.
I would do the following:
Remove the bodge the RAC guy did. I can't imagine what he was thinking but there is no need to bodge the wiring in this way. Put it all back as standard and replace the light bulb in the dash if it's blown.
Remove the battery (taking care that you have the code for the audio system first) and fully charge it on a decent mains powered charger. Check that it sits at 12.5-12.8 volts once it's fully charged and has had a little time to settle.
Put it back in the car and go through my guide posted by AndyB to see if it's charging. If it's not I'd remove the alternator and get it checked by an auto electrician in case the RACs bodge has killed it.
If there is an alternator problem it is most likely just the regulator pack which can be replaced without scrapping the whole alternator.
While you're at it, check the leads from battery to starter, alternator, chassis and engine block are sound. The crimped connections on these thick wires can work loose and cause a voltage drop.
I suspect all of your issues with the gearbox, etc. have been due to low supply voltage to the relevant ECUs.
Kevin