Sorry so long to get back to your question.
It sounds to me like you've got a pretty good deal in the works. A couple of things about working with the city.
Check to see what permits, if any, are on file for this property. If they were undertaking a large scale renovation, it's unlikely they didn't have any permits issued. The again.. it has happened. You can check on the permit history at any satellite office for dept of buildings. You will want to call ahead and find out when they have "walk-in" hours to sit down with a plan reviewer to discuss.
Another way to go, and I will recommend this as the best way to go, is to get an architect involved. You will likely need to get one involved anyway to get permits for an extensive renovation. You can discuss your zoning questions with the architect and get answers that other will not be as well versed on. Usually an architect will be glad to give you a fixed price contract for the drawings, which you will need for the permit (you may not have to do the plumbing and the electrical over again if their able to be brought up to code and you can get the city to approve the plans your architect draws, with existing plumbing and electric in mind). Architect's often offer expediting for your permits. If time is crucial, then pay for the expediting. If you have time and want to save money, you can expedite the plans yourself.
As far as zoning is concerned, I agree with Scott and that having the local political muscle behind you is helpful. I will add that the city has very clearly defined zoning districts and that getting a variance can be very costly. It is likely, that if what existed was a 3 flat, and you want to put a 3 flat back together, zoning will not be heavily involved. If you are adding units or square footage, including a basement, zoning is likely to be involved. How complicated it will be is a matter of what's there, what permits have already been issued, and the exact zoning and the survey. An architect can help you with a feasability study to determine home adding sq.ft. or units will be viewed.
Conversion is a matter for an experienced attorney or consulting firm. It is less complex for a three unit building vs. a six, though.
When recruiting help with the process, experience counts. The city would like to see you succeed in rebuilding a foreclosed building, and in this economy, they will be grateful for the permit $$$. You will likely need expert advice, so get it before you can't walk away from the deal.
Best of Luck. You can contact me for referrals. I know lots of good builders and architects.
The permits are a way of life. Again, your alderman will be a tremendous help on this and will help you speed up the process if he's on your side.
I can happily recommend an attorney to you but I am not comfortable posting his information in a public forum without permission.
I'm an experienced agent who has helped numerous builders- including 2005 Chicago Builder of the Year Foreit Properties- though every step of the process up until they're all leased out or sold. Contact me privately more for information but I know I can help you.