First I want to apologize for putting this here but couldn't find a better section to write this. I would like to know, if I block someone, do I still appear on that person's friends list or the name disappears from their list at the moment when block happened?
Don't worry about posting in the wrong section. You're more or less right to post it here. If you're blocking (ignoring) a person who's in your friend list then they will be removed and put in your ignore list.
you won't appear on their friend list if you remove them from Your friend list. if you aren't sure, unblock then see if that said person is still on your list; remove them if needed.
if you happen to run into them randomly, then you can Ignore them.
I'm not sure if hitting 'ignore' also removes them from your list. maybe someone else knows that can reply?
A person on your friends list you block will be put under your ignore list. If you decide to unblock that friend, he/she will not go back under your friends list. That person will be deleted instead.