remove search bar

Go to to Settings>Siri & Search>Siri Suggestions>Suggestions in Look Up and turn it off. That should prevent website answers from appearing on the screen.

Or, use Guided Access.

Use Guided Access with iPhone, iPad, and iPod touch - Apple Support

Or, just don't allow him to use your phone if you can't trust him to obey your rules.

You cannot remove the search bar from the spotlight search page. That would defeat the purpose of the search page.

Just do not access it if you don't want to use it. You can't remove Spotlight Search from an iPhone.

Put a passcode on your iPhone.

But, unless he has the passcode, he won't be able to open anything he searches for.

Then put your phone where your children can't get to it.