Unfriending,Privacy settings

So let's say you unfriend someone well from what I see they still appear on activity feed like ''bla bla is playing this'' even if I don't have them friended I feel like that's kinda stupid since I don't know the person at all and unfriended them or blocked so if you could fix this then I would be very happy
Second thing is I have my privacy setting to scan direct messages from everyone I unfriended this person and a stranger is messaging me and I also have it to nobody can add me so yeah these are the two suggestion I have