How to keep my iPhone screen on for a longer time?

Go to Settings>Display and Brightness, scroll down to Auto-Lock and change the setting. Be patient, this is a user to user support forum and someone here has to read your question and type an answer, and that can take much more than 2 minutes.

in the Display and Brightness you simply set the desired time for how long the phone is turned off

I have a question about Screen Time: I don't want to save my activity in screen time temporary, but when I turn off and turn on screen time all history was remove, What can i do

Don’t turn it off then on.