My engineer office is a few weeks out on survey, but I have permits in hand and my excavator wants to start ASAP. 

First thing I will do is make sure a dumpster is there day one and also make sure we have any permits ready to submit once it is officially ours but is there anything else we can really do to get a jumpstart and stay ahead of schedule?

no.Is it done all the time, especially in Miami.....yes.There will be no way to get it permitted and do it legally....single family zoning will prevail.

I don't know (recall) if they are in local ordinances but I do recall vaguely seeing some legal / ordinance type of material detailing when it can and cannot be done, regarding building in a way that directs water towards a neigbors property.I don't know Chicago that well, but as a homeowner I would try calling your local building and permit center and see if one of the local inspectors can direct you to the code section to read.I'd do that before anything else because knowledge of those ordinances will arm you / prepare you best to approach the other parties.With regards to the possibility of 'dealing' with the water, I'd be thinking about ways to do that, too - in the event that the above / negotiating an alternative solution is not fruitful. 

On top of that you'll have permit fees 1-5k, engineering/design 10-20k, tap fees 5-15k, landscaping, driveway, financing costs, costs to sell etc. so I don't think you can get the numbers to work with any profit or equity built in unless you could expect the price point to be well over a million, closer to 1.5 really. 

You got permits and approvals for all the work, right?

The Building Inspector (Elect.) spent 2 hours checking every circuit before signing off on the permit. 

With permits the total cost of this job was just under 11,000.00  Shortly after this feces and toilet water started backing up into both units.

The property is currently at 982 sq feet however has an 288 sq foot addition not permitted with the city yet.

We have considered renting but we had some work done on the house that was not permitted so it is a big concern for us in renting it out.