iPod touch Problem syncing apps on 1st gen itouch

Got a previously owned touch from eBay for my daughter. Everything works fine, synced it, apps are on there running great. But now when I connect the iPod to the computer the apps tab is greyed out and it won't let me sync any new apps, or uncheck the box and not sync any apps at all.

And also, is there supposed to be an app for the app store on a 1st generation itouch?

Thanks! Kelly