Q: How to prevent  child from turning off "Find my iPhone"

Apple has an free application in the Mac App Store called Apple Configurator 2. It is designed for companies to setup company owned iOS devices and lock them down. You could probably use it to set up the devices for you child in a configuration that will lock down certain functions like blocking the ability to turn off iCloud features like Find my iPhone while still giving him the ability to use the password for store purchases.

About Apple Configurator 2.0 - Apple Support

Here is the help guide to walk you through how to use Apple Configurator 2

https://help.apple.com/configurator/mac/2.0/

You can use a different Apple ID for Find My iPhone than you do for making iTunes purchases. Set up a different account for Find My iPhone and don't give your child the passcode.

iTunes/App Store is the same as iBooks and Music.

You can also take a look at Family Sharing. I believe it will give you some additional options.

You can set up restrictions in Settings > General > Restrictions > turn Enable Restrictions on (it will prompt for a 4 digit code) > Location Services > Don't Allow Changes same for Share My Location (if applies)

I also use Family Sharing and my son has his own account for the App Store, so he cannot change that or download things without me or my wife knowing.

EDIT: Link added for clarity Family Sharing and location - Apple Support

Sorry for double posting, but much clearer if you do this in his or her device

Settings > General > Restrictions > Enable (add 4 digit code) > Accounts > Don't Allow Changes

iCloud will be greyed off and unaccessible unless you turn restrictions off again.