Cold Starting?

I have an R reg. Ford Fiesta fitted with a diesel Endura DE engine. It has recently developed two faults. One is difficulty starting when the car has been left standing overnight. Once started and warmed up after travelling a short distance, it behaves perfectly. The second fault is that after a difficult cold start and then turning off the ignition without moving the car the engine continues to run. If I drive it a hundred yards or so, it switches off as normal. I would welcome advice on whether these two faults could be inter-connected. In other words whether the fuel shut-off solenoid is not only failing to shut off properly but is also failing to let fuel through at initial starting. I’ve been told that a fuel immobiliser is an integral part of the fuel pump but the Haynes Manual only mentions a fuel shut-off solenoid which can be taken off separately and replaced.