How compatible is the OS with 'normal' android apps? Since 4.4 I have been able to, at least to some level, revoke some basic rights that apps have, like seein

How compatible is the OS with 'normal' android apps? Since 4.4 I have been able to, at least to some level, revoke some basic rights that apps have, like seeing my contacts (through app shield or whatever). If I am able to download apps from the 'normal' Android store, is access that those apps have somehow controlled as well? Some sort of sandbox mode would be nice.