1) sort of. You can capture spirits, that you can keep in little glowing cubes, or sell at the science facility. Actual ghosts are banished/convinced to depart, not kept by the sim.
2)n/a
3)yes sort of as described above.
4)not sure, I've never tried. I would suspect not in most cases (see my answer to 6)
5)I wouldn't think so, but I've never tried it.
6)when you reach level 10 the sim is given a device that allows you to find spirits anywhere in the neighbourhood - I think you could keep this device as it actually shows up in your inventory, but once again, I have never tried leaving the job after level 10.
hopefully someone can give you better answers