Can my landlord give the keys to my apartmentto a friend or relative of theirs for a building fire inspection?

A landlord is *not* obligated to personally do all the work--inspections, maintenance, showing the premises, etc.--but instead may either hire someone to do it for him or delegate the role to someone else.

Of course, that person is subject to the all the same requirements as the landlord in conducting the inspection (or performing maintenance, etc.), such as proper notice, only during reasonable hours, etc. And if the person either deliberately or negligently causes injury or loss to you (e.g. steals something from your apartment; forgets to lock up or loses the keys, so someone else can come in and steal; etc.), then both the landlord and the person who acted in his or her stead could be liable to provide compensation.