Is it possible for someone to screen share or nirror the screen of an iphone remotely or without permission?

Hello,

No, that would not be possible unless the other person previously had physical access to your phone and knew the screen unlock passcode.

See this:

https://www.apple.com/airplay/

Good luck.

Hello,

In that case, do this:

1) Perform a factory reset: Restore your iPhone, iPad, or iPod to factory settings

2) Set a screen unlock passcode: Use a passcode with your iPhone, iPad, or iPod touch - Apple Support

3) Change your Apple ID password: Change your Apple ID password

4) Do not let anyone else have physical possession of your phone.

Good luck.