Open My Profile, then Edit profile. Only me keeps your profile private. Friends limits access to accepted friends. Everyone makes your profile available to anyone with its link. Your email address and login details are never part of your public profile.
Discovery is a separate choice. Enable it to appear in player search when your visibility allows the person searching to view your profile. Private profiles do not appear in global search. Exact-handle friend lookup follows the separate discovery setting.
Blocking another account hides your profile from that signed-in account and removes the friendship. A public profile is still visible to signed-out visitors; use Friends or Only me if you want to restrict access.