NTFS and FAT have different permission models than Unix. This especially means that there is no executable flag on such a file system. Calling
chmod a+x FILE is a no-op. Linux emulates classical Unix permissions on NTFS file systems by setting a mask for each file that contains the would-be permissions.
To fix these problemss, either move executables to a different file system or change the mount flags to use a permission mask that enables the executable-flag (for all files).