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Deleting apps from the iPhone is the same process in iOS 7 as it was in iOS 6:
I would suggest signing out of your iTunes Store account; and restarting and/or resetting the iPhone:
If that does not resolve your issues, refer to page 146 in the iPhone User Guide to Reset All Settings:
iPhone User Guide for iOS 7
Here are some additional tips for the iPhone 4S
I have the same problem as charmainefromgbr. I installed WhatsUp instead of WhatApp and now I cannot remove WhatsUp. Whilst I get the wiggles I am not getting the crosses as I used to before. I am still on IOS6 because there was not enough room for IOS7.
did not address this problem