Actually not. M87 is a 1000 times farther away than Sgr A* but also a 1000 heavier and thus a 1000 times bigger in diameter. (Diameter/radius scale proportionally with the black hole's mass.) Therefore, the actual angular size on our night sky is the same for both black holes and, from this point of view, both would be equally difficult to observe.

However, as they mention in the press conference, Sgr A* moves a lot faster relative to us than M87, so it's much harder to take a still image. (In the press conference they used the example of trying to take a photo of a toddler with an exposure time of 8 hours.)

During the press conference, they said photographing the M87 black hole was like shooting a hibernating bear, and photographing the Sag A* black hole of our galaxy like photographing a quickly moving toddler. Something about the speed making it much harder. It is also much smaller, but that's less of a problem because it's much closer. All in all apparently making it about the same angular size. But it sounds like they'll get to it, it's just harder.

M87's black hole is currently eating something big, which makes it brighter. The black hole at the center of the milky way doesn't seem to have eaten anything lately, so it's accretion disk may be small or nonexistent.

Nope, for the same reason we had photos of the Moon before we had photos of Earth.

Nope. The view of our own galaxy's supermassive black hole is completely obstructed by matter within our own galaxy. You can't see to the core of our galaxy; it's too dense. You'd have to send a rocket quite some distance outside of the galactic plane to get a good view of it.