Is someone remotely accessing my iPhone? Can someone watch you on face time auto without you knowing it?

On my iPhone there are calls I never made and the light turned on by itself saying facetime with a number by it. 

Is someone watching me and using my phone?
The number by FaceTime simply means you missed a Facetime call. Just like missing a 'regular' phone call, someone tried to call you using Facetime, and you didn't answer.

There is no security risk here, no one is watching your phone or snooping on you. Someone just tried to call you. 

It is likely someone did this by mistake. On iPhone, you can easily Facetime from the Contacts app, and the Messages app, without meaning to. It is convenient, if you intend to Facetime with someone. Otherwise, it is simply and icon you never touch again!