File permission os SD card (FAT32) Android uses FUSE for SD cards. Does FUSE support file permissions for SD card? If no - how do I install some apps on SD card? Cause there is no support for symlinks, execution permission etc.
Usual (FAT32) SD Cards do not support permissions, they allow everything because they are only mass storage and were never designed for such advanced things.
You can of course format your SD Card with a compatible file system (ext4 for instance) that supports permissions.
FUSE does not support file permissions because it just wraps around an incompatible file system. Changes are unsuccessful because there is nothing where you could save those permissions.

Apps on SD card are also not on your external SD Card (FAT32) bit on yourinternal one (ext*) which has support for permissions.