I don't get how this is connected. That person never downloads anything without my permission. And how would us having the same apps help somebody else to install a hidden application to my phone?
As I already said, I believe that the person could have just gone to app store from her account and downloaded it to my phone, as she had an access to my phone for several hours without me knowing it. The problem is not how she got something on there, the problem is, I don't understand why wasn't it visible before or showing any signs? There were no new app icons, itunes never asked me to authorise that account. There was no hint of anything thirdparty being installed, untill today's weird request for a password about I don't know what. Also I don't understand how is that possible when my phone isn't jailbroken. Is apple allowing such kind of apps?