What happens, if the application, for which access to the storage is allowed, runs other application? Will this other application be able to access the drive?
The answer depends on how the access is granted. If you grant access only to the certain process, then the children of this process won't be able to access the drive. If you grant access to the process and all it's children, then any application, directly or indirectly started by the granted process, will be able to access the drive.