No
No, if you block someone on Facebook, they can not see any of your activities
To remove someone from your Facebook you unfriend them and if that doesn't work you can block them. That will take them off.
You can stop someone by sending message only by blocking that person from your Facebook. Messages will only be stopped when you block the person who is stalking.
No.
search their name with a different facebook account.
Ok this is really simple just unfriend them or block them.
When someone has blocked you from their Facebook, you won't be able to know if they have also deleted you.
When you block someone on facebook they have no access to anything of yours on facebook. If they type your name is search nothing will come up. If you and the blocked person have a friend in common and you post something on your friends page and the blocked person see's it your name will come up as Facebook user. As well when you block someone you are blocking yourself from them aswell. So the same rules apply to you aswell.
You can report the person on Facebook and the relevant authority if you get cyber bullied.
i'm not sure u can but u can block them or appear offline
I am looking answer for this question too. Maybe Someone will write a facebook application to do. Such an application will be very very usable.