The entire structure would probably need to be furred out from the outside walls in, making thicker walls and deeper window wells, in order to insulate it to current building codes and to be able to pass inspection---AFTER you rewire it and replumb it to also pass inspection as a multi family structure. That will take away from what is already planned to be a pretty small residence area, but it is all necessary. Sprayed dense pack cellulose will have the greatest sound deadening properties, coupled with double layers of drywall on both sides of the internal walls. Your local municipality will need to determine if the walls need to be fire walls though, so check with them before even beginning the project. Be sure you have the proper insurance in place to protect yourself.

Also double check to make sure that you only hire licensed and insured trades professionals for the project. Multi family buildings have additional requirements beyond single family homes due to more lives being at risk. And unless the homeowner is also a licensed trade, then he cannot work on the building's systems. To turn the building into a multi family dwelling, you will also need to file to have the zoning of the property changed. If you don't, and get caught by your neighbors, you'll face fines and possibly even jail time.

There is a GREAT deal of personal risk to you if you do this project incorrectly or "off the books".

Are we to assume that this project is to be constructed without a building permit and without the stamp of a licensed design professional?

We are in the process of interviewing several professionals to complete the job. I would like to know the questions I should ask and what should I expect them to know regarding insulating. I'm always skeptical when hiring people to do certain jobs. Some men seem to view women as damsels in distress.

Hire a woman architect.

The issues you raise are controlled by fairly strict building and energy codes so ask the architects how they would meet those requirements and if they recommend exceeding them. Your town may even have a local code increasing the level of energy conservation required.

So, their solutions will probably depend a great deal on the existing conditions, codes, and your budget of which we know little to nothing.

The floor/ceiling assembly between dwelling units should also have a fire-resistance rating which means any penetrations like recessed lighting will need fire rated enclosures and acoustic separation may require resilient ceiling channels. Entry doors will probably need to be rated and the egress stairs may need to be modified if they serve more than one unit.