Can I install the "app store" in an IOS simulator?

This is NOT possible

The Simulator does not run ARM code, ONLY x86 code. Unless you have the raw source code from Apple, you won't see the App Store on the Simulator.

The app you write you will be able to test in the Simulator by running it directly from Xcode even if you don't have a developer account. To test your app on an actual device, you will need to be a part of the Apple Developer program.

You can install other builds but not Appstore build.

From Xcode 8.2,drag and drop the build to simulator for the installation.

https://stackoverflow.com/a/41671233/1522584

No, according to Apple here:

Note: You cannot install apps from the App Store in simulation environments.