Question

Is it possible to show a modal view controller in iOS 6 that present my app in App Store?

Answer 1

Yes you can. (iOS6+)

Take a look at SKStoreProductViewController

NSDictionary *appParameters = [NSDictionary dictionaryWithObject:@"533886215"
                                                          forKey:SKStoreProductParameterITunesItemIdentifier];

SKStoreProductViewController *productViewController = [[SKStoreProductViewController alloc] init];
[productViewController setDelegate:self];
[productViewController loadProductWithParameters:appParameters
                                 completionBlock:^(BOOL result, NSError *error)
{

}];
[self presentViewController:productViewController
                   animated:YES
                 completion:^{

                 }];