hey Darklin, are there any other faults stored? nothing thermostat or coolant temp sensor related? the R56 can do weird things when there is a fault there.
Claire, all the faults stored point towards a bad inlet vanos solenoid valve, infact that fault code 2845 says exactly that.
Check it's plugged in, I could maybe take a picture of one tomorrow to show you where it is if you like? it's at the back of the engine, drivers side top a silver cylinder looking valve with a black plug.
I suspect you need a new one, fairly common for them to jam up internally and need replacing. it's messing with the valve timing.
otherwise it's possible the timing isn't correct from when the chain was replaced, hopefully not