Try creating a new Administrator-type user account and see if the problems persist. If they do not, then your current user account may be corrupted, and you should migrate your settings and files to a new one.
If they do, fire up an elevated command prompt and run "sfc /scannow."
If this solution does not work, right click on your C:\ drive and select "Properties." Go to the Security tab. Click "Edit." Select "Add." In the text box asking for object names, type ALL APPLICATION PACKAGES. Press OK, then select the new entry "ALL APPLICATION PACKAGES" and, under Allow in the box below, click "Full Control." Press "Apply." PERFORM THIS LAST SOLUTION AT YOUR OWN RISK. This gives downloaded apps from the Store complete access to your computer.