At night, as soon as I plug my iphone to be recharged, my iphone starts behaving abnormaly. It is like somebody has taken control of it. I see the screens moving, music starts playing and then stopping, etc.

Question

At night, as soon as I plug my iphone to be recharged, my iphone starts behaving anomaly.  It is like somebody has taken control of it.  I see the screens moving, music starts playing and then stopping, etc.  I have noticed that several nights.  What I do is in Settings is to change  into Plane Mode, thinking that, may be if I do that, somebody that has taking control of it will not be able to download data.  Yesterday night, I was awakened by an alarm, whose setting I did not changed. When I looked over, the alarm screen changed to Settings and the Plane Mode changed alone in front of my eyes, from on to off.
I have not observed such a situation during the day. Only when I plug the cable.
I suspected that may be there is no Trojan installed. May be the cable, which is a spare cable, has been modified by a hacker, and it has electronics installed in the connector.  But tested with the original cable, and the behavior was the same, as described above.

Answer 1

Thanks Meg for your reply.
It could be that both cable are bad. But, anyway, you would not expect any of these manifestations, even with a bad cable. I had bad cable for my 4s, and never saw such a thing! 
I contacted by chat the support of Apple.  They told me that this behavior could be a software problem and recommended me to do a full recover of my iphone. That meant, putting in at the factory conditions and recup all the data from the backup.  I did that, and the behavior did not change.  The backup was made with the data of my PC, not icloud.  Tomorrow will try with icloud and check if that will work.