Graffiti is something written on a wall, and, of course, art can be exhibited or produced anywhere: a wall is just another venue.
Art and society was a lot more subject to sexism 50 years ago than it is now. Since that period, there have been plenty of very good female painters, 2006 Turner Prize-winner Tomma Abts among them. How much history needs to pass before an artist is called 'great'? That is the real question.
Duchamp's urinal was art once he put it in a gallery. In fact, one working definition of art is anything that is in a gallery.
Movements are overrated and invented by the press. Ask any artist if they feel or felt part of a movement - the good ones will all say no.
Art is about the context in which it is made as much as the object itself; objects take on different meanings in different contexts. If the artist is unaware of the context, it's very unlikely the work will be very good.
Street art is designed to be seen out of the corner of your eye, on the hoof. Art that's made for galleries is made to be looked at in a more static way for a longer period of time and may not be so striking immediately, but perhaps resonates for a longer period.