Is it permissible to teach one's brother something on the computer using a non-original operating system, and is it permissible to learn from him if what he learned was acquired through this system?

If you are among those who believe it is forbidden to use pirated discs without the permission of their owners, then it is not permissible for you to help their users on how to use them, because that is considered aiding in sin. However, learning something from what the user of those discs knows is permissible.