If you mute a player, can he still read you in the chat?

Yes they can still see your messages you type. You muted them, but unless they mute you, they can see your messages. I know this from duo queueing with people.

Has we can see here yes, they can still read your messages, because YOU muted him, HE didn't, you don't see the messages of someone you muted but they are able to see yours, also, if you for some reason mute a friend and don't remove the mute he will automatically be removed from your friend list (At least used to work like this, lost some flaming friends like this)