Couple thoughts.

  1. If the entire city is able to go to the arena, I think it is going to have to be much larger.
  2. If the culture doesn't have any superstitions or religious anxieties about the dead than your placement is ok, but if they do, would people really live that close to the dead (or potentially undead )
  3. I wouldn't worry to much about the estates. If you think about it, only so much wealth can flow into a given city, and probably only 1% of the population will really hold the largest portion of that and it will trickle and move about through the middle class and finally to the poor. So the question becomes just how much wealth is there and who are they? I would imagine that there aren't that many nobles in a city of this size.