Because their programming limits them to the Milky Way.
That's really all they are meant for. As machines, they are the pinnacle of evolution, in their creator's mind, and have not advanced past a certain point.
No soul, replaced by tech. No culture, replaced by tech, no limitations and thus need for advancement, as Mordin puts it.
The Reapers have no need to go to another Galaxy when their mission requires them to stay in one, so they had no need to advance their technology to go beyond it.
They probably could, since they likely built and maintained the Mas Relays and have infinite patience, but they had no need to, so therefore they did not do it.
Possibly. But if the Reapers really do have a mandate to preserve organic life against a synthetic threat, then logically they would have a need to worry about Andromeda too.
If they believe that organics will inevitably create a runaway AI singularity that would destroy them, then they would believe that one or more of these things must exist in Andromeda. And if these AIs are allowed to evolve to a point where they rival the capabilities of the Reapers, and if they are aggressive and expansionist, then the Reapers should start to worry about them turning up in the Milky Way and slaughtering all the species they were supposed to "protect".
Therefore the Reapers should really be out in all of the Milky Way's neighbouring galaxies that they can reach, nipping potential AI singularities in the bud.
Edit-and, if I recall correctly, astronomers predict that Andromeda and the Milky Way will actually merge in 5 billion years or so, which would be another reason for them to keep an eye on the place given the timescales they work on.