As we know, graves in masjids are not allowed, and I have also read that conducting business in a masjid is not allowed.

What exactly is considered the masjid in this instance?

If a masjid is a building with a few smaller, but connected, satellite buildings, and the whole area is surrounded by a wall, is the whole walled off area considered the masjid, the built up areas, or is it just the main prayer hall?

The Permanent Fatwa council in Saudi Arabia defined the masjid as being the place that is set aside for prayer. Therefore, an Imam could have a house or an office on site but it would be considered to be outside the masjid. Therefore, business can be carried out in the Imam's house or office outside the masjid or the place or hall specifically set aside for prayer. Graves are supposed to be at the graveyard and not at the masjid or in the yard or compound. Having graves at the masjid is means of shirk. At times the masjid fills up and people will have to pray outside so that would not be right when a grave is on site.

And Allah knows best.