Facebook – Post from Facebook Games not showing on the feed

If they are on your "Close Friends" list then by default you will be notified whenever they post. To turn that off, click on "Close Friends" in the left sidebar (if it is not there then click "More" next to "Lists" and then click "Close Friends"). Then click on "Notifications" at the top and choose "Off". Of course you could also remove the person from your "Close Friends" list.

Groups are the same way. If you do not want to receive notifications for posts to the group, click on the group name, then Notifications at the top of the page and choose "Off".

It sounds like the user has blocked you. In that case you cannot see their posts or comments or their profile and also they cannot see your posts or comments or profile. You will not be able to block them except by email address, but they are already effectively blocked so there is nothing you need to do.

Of course, if they have a friend or family member that can see the post then that person may have shown it to them, or if the post was public then they can see it without even logging in.

In the past it was possible for someone to block you so that you could not see them, and then they could log in when you are not on and unblock you so that they could read your comments, and then block you again when they were done. To stop that, Facebook now requires that you wait 48 hours after clicking on "Unblock" before they are actually "unblocked" and also you can't "Block" the same person for 4 days after clicking on the "Unblock". So if someone is blocking and unblocking you, you will have at least 48 hours to see them (and block them if you wish) before they can block you again.