K12 Timing Error Again Or Could It Be Something Else

hi there all joining this site on behalf of my sister in law she has recently purchased a K12 1.2 3 Door. Despite all my informations and warning she went along with my father in law and brought a car with a engine warning light. When i first saw the car and heard the engine my mind was at rest but i got a message from her saying she couldnt start the car.
The problem she had was that when cold the engine would start at fire first turn of the key. She had her problem when she turned her car on moved it off the drive then went to turn it on again 10 minuets later and struggled to start. My first thought over the phone was she had flooded the engine as sound something my old civic liked to do if the thermostat hadnt ticked on before turning off.
She brought the car over to me for me to have a look, i scanned the ecu and came back with p0340 (cam sensor). I thought the worst for her when this came up but i listened to the engine and no rattles what so ever. I cleared the codes problem remained, so i took the covers off and checked the timing chain and tensioner and are well within tolerance. So i thought it would come down to the cam sensor what i wanted to know before i order the part for her and fit it is could there be any other issue.
I did some research and found that one guy (cant remember where) had a problem with the coolant temp sensor playing up when the car had been run for only a few mins. This causing the ecu to have a fit and causing p0340 to throw up, after new coolant sensor engine to run fine.
Sorry for the long post but thought the more information i put the better response i may get.
The exact problem is that starts first turn no rattles no nothing. If turned off before fully warm (2-3 mins) the car struggles to start sometimes starting then have jumpy revs. If car has fully warmed up can be turned off and started straight away or left till cold and then starts fully only when it has only just been run for a minuet that there is an issue. If anyone else has found this problem with the possible coolant sensore please let me know before i buy a cam sensor that may not be needed. My experience with chain engines was only with an S type Jaguar which engine was bulletproof and chain changing was around 150k. The car is only on 60k.

once again sorry for long post any other information need please reply and i will respond many thanks.
 
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