Q: Some Phone calls and Messages going to previous owner's phone

Did you remove it from FaceTime?  There is a setting to "ring on all devices", and it's tied to the FaceTime account.  This will not be logged out when you remove iCloud and iTunes.  Same goes for iMessage

It sounds like the previous owner did not properly prepare the phone to be sold / given away.

This is what she should have done: What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support

It really needs to be properly prepped for you, then you need to activate it and set it up with our account.