Thanks for your reply. Yes the symptoms you explain are what I am experiencing.
I spoke to the place I bought it from today, they are a small Indy Garage who had maintained the car for its previous owner for many years. less than 10k miles ago & about 2 years ago the gearbox was removed, stripped, speed sensors & solenoids replaced then re fitted, I also have the original invoice for this work, the Garage said that as this work had been done, it is extremely unlikely that these components would fail again as improved ones are fitted as replacements.
That would hopefully eliminate 4 of the problems you list.
I can check the Engine Coolant Temperature sensor & see if its connected.
The garage did say a common fault is the wiring that goes from the gearbox to the control unit thats behind the glove box can let water in & makes the connection to the control unit wet often leading to problems, so my first check is to see if any water has come in!