Question
Permissons inherted from Parent
soln
Those settings are correct to give User A full control of that folder. If you want to reset all permissions under that folder then check the "Replace permission entries on all child objects..." under Advanced. Keep in mind that this will wipe out any customized NTFS permissions set on subfolders.
2. In order for it to show up that way you would have to grant User A full control of C:\Program Files. It doesn't sound like that's necessary. Permissions are additive, so having inherited Read & Execute does not interfere with having explicit Full Control.
What errors come up when the user tries to run the program? It's likely that it needs access to registry keys and files outside that folder. You can use Regmon and Filemon to determine exactly what it's trying to access.
http://www.microsoft.com/technet/sysinternals/utilities/regmon.mspx
http://www.microsoft.com/technet/sysinternals/utilities/Filemon.mspx