You can either sign a POA as @Jennifer Petrillo suggested or you can sign the closing documents (deed, etc.) along with an authorization form (a very limited POA) and the attorney can sign the closing disclosure document at closing. 

Does the new owner have to honor the current lease agreement with the Chicago Housing Authority?

If you google "HUD-VASH your local city/county name," you will probably find the local housing authority that administers it (local to me it's the same people that do sec 8).

I would reach out to the local authority having jurisdiction.

"Any hydrostatic testing must be separately authorized by Seller in writing"The test failed and now they are using this as leverage (obviously).

If your agreement does not give them authority to set the rental rate, you may have an argument to pursue them for damages, assuming they set rent too low.

The downpayment is $47,000, now in Canada, the 5% cash back is going in as cash directly to my Pre Authorized Bank Account linked to the Mortgage. 2 - What is the difference, in actual $$$, in mortgage payments during the first 5 years between the two options?

Taxing authorities may not foreclose if the property is worth far more than the taxes owed because the penalties and interest often provide a double digit return

Although I wouldn't call myself an authority on the technical history of residential construction here, I'm not an amateur.

I also like to read a lot and have found several great books on real estate investing through BP and other authors.