Everything is on the Friends page.
Finding someone
Search by name or handle under Find someone, then Add friend. They get a request, and nothing changes until they accept. Requests waiting on you appear under Waiting for you with Accept and Decline; ones you have sent sit under Asked, no answer yet and can be canceled.
If somebody does not come up in search, it is usually because they have turned off being findable. That switch is Settings → Privacy → Let people find me in search and on Discover, and it is yours to turn off too. A direct link to somebody’s page works either way. Find friends shows everyone who has chosen to be findable.
Close friends
Next to each friend is a star reading Close. Turning it on lets that person see posts you set to Close friends.
Removing and blocking
Remove unfriends somebody immediately, with no confirmation step. They are not told. They also disappear from your top friends strip straight away.
Blocking is stronger: a blocked pair cannot see each other at all, including posts set to Anyone, and it holds everywhere — a blocked person will not reach your posts through a mutual friend’s page, and cannot message you. Any conversation the two of you had leaves both inboxes; unblocking brings it back exactly as it was, because nothing was deleted.
Block is on the Friends page next to each person, and on their profile. It asks once before it does anything, because it cannot be undone from their page — once the block is on, their page is not visible to you either. Unblock lives in the Blocked list on your Friends page.