Transit mk7 rough idle,radio requires code all the time

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Can anyone help me?My 2009 lwb hi roof mk7 2.2 Transit has rough idle type of hunting,it also loses the radio code every time the ignition is switched off and the interior light only works with ignition on.when you open the door the interior light does not come on till you turn on ignition.Is there any links with all these problems?
 It seems to run ok on the road with plenty pulling power although I do believe it is limited to 70 miles per hour as it will not exceed this uphill or down.The engine is the 110ps.one other problem is central locking does not work with the fob.am I correct in thinking they do not have a battery fitted.I have read about egr valves,clutch pedal switches and fuel regulator problems but don't see anything on the radio etc
 The van has covered 122k with service history.Any other problems these engines are known for?Cant think of anymore to say but forum insisting I write 200 words.think I have said everything I can think off now,The van is fitted with some kind of inverter in rear wired to 240v sockets but I don not see that it is causing the problems.if anyone can throw any light on this much appreciated.
 
 
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