How to restrict Google Searches on Safari?

It's not entirely clear to me whether or not you understand you are not addressing Apple on this website, so before we go any further you might wish to review how to use this site, here: Find answers and ask questions in the Apple Support Community - Apple Support. If you would prefer to address Apple directly there is a link at the bottom describing how to do that.

I understand that you want to restrict the use of your child's iPhone, so I suggest you begin by reading Help your child set up an iPhone, iPad, or iPod touch - Apple Support. As a parent you have essentially limitless ability to impose appropriate restrictions on what your son can do with it.

For example, if he were to attempt a Google search using Safari, the following would result (the screenshot is from a Mac but the idea is the same):

... and that's the end of that.

As far as Google Maps and how it relates to their YouTube product, I'm not the best person to ask because I explicitly prohibit the installation of any Google products on the Macs and iPhones / iPads by anyone in my organization. To my knowledge though Google Maps has to be downloaded as an app, and you can certainly prohibit your son from accessing the App Store.

Start by reading those setup instructions, and if you need additional guidance from your fellow Apple product users by all means please write back.