Can I disable automatic "copy/look up/share" on my iPhone SE?
It's not automatic, it shows when you highlight some text, by holding down on a paragraph of selectable text. It's not possible to disable this action.

One failure mode of the digitizer is that it will select areas on the screen randomly - if you open up an app like the calculator - if buttons there get pressed randomly when you aren’t actively moving a digit on the screen, that’s a good indicator your hardware is failing.