On your iPhone, your phone number and Apple ID email address are the default ways in which somebody can contact you on FaceTime. While you can't remove your phone number as an option, you can remove your Apple ID email account. More importantly, you can add any other email addresses you'd like to this list, so you never have to worry about a friend, family member, or coworker not being able to audio or video chat with you.
When you're taking a video in the Camera app on your iPhone, there's a little white shutter button in the corner that lets you take a still image while you're filming. Apple brought that same concept over to the FaceTime app in iOS 11, iOS 12, and higher, so you can take Live Photos of your friends during video chats.