Student - no teacher.
I once heard one say "he did it with facility." And she meant without an effort. Don't know if that is correct.
Amenities are in my opinion not only things you can touch or see such as good furniture or equipment. It is also the atmosphere or sound....so your guessing is right for me. It contains more than facilities.
As stated above - I am no teacher...let's wait for an expert meaning.
Bye