Several problems with this car all started at the same time.

Firstly, when cold the engine starts first time and the car drives as you would expect. Once warm however, the car goes into limp mode and is difficult to get over 30 mph unless going down hill. Also when warm the car will not start first time and run. It will start but stops almost immediately. This must be repeated two or three times before the engine runs normally. At about the same time we noticed an oil leak –not sure from where- and found the oil level seriously low. Topping up did not cure the problems. No warning lights are showing so, can we have your opinion as to the cause of our problem please?