Q: how do i restore appstore apps to my phone?

Hey Paul, 

I understand that you aren't seeing the App Store on your iPhone and are also having an issue removing apps within iTunes. Let's see if we can get it sorted out. 

I would start with taking a look to see if you have any restrictions enabled on your iPhone. One of the restrictions is installing apps and that would remove the App Store from your iPhone. Another option is deleting apps which also might explain why you can't remove apps by using iTunes. Also note that if you don't know the password to disable the restrictions, that you will need to restore your iPhone. Take a look at the article below for more details.

About Restrictions (parental controls) on iPhone, iPad, and iPod touch
https://support.apple.com/en-us/HT201304

Take it easy