I use this service to find out in one location loans on a house, any permits filed, comps.

Which government agency(or multiple agencies) is ultimately responsible for permits?

3 choices...Live with it, hope you never get caught...make sure it’s up to code for liability issuesGet it permitted, if zoning allows.....will involve getting permits, inspecting, modifying, tearing out portions to rebuild to codeTear it down

Does anyone have experience with paying an hourly rate for a professional engineer to make necessary permit drawings in Ohio?

You do have to manage the project and the builder, and you just do the permitting yourself.

I estimated a repair period of one month before I noticed a lot of issues with the house.We applied for permit at the city, and we were told that there was no construction permit or plans for the house with the city.

Since 2006, housing permits for new homes has been significantly below population growth - entering 2019 with San Diego having an estimated 59,000 shortage of dwelling units.9.

Do you have data from the county recorder on what improvement permits have been issued for this property, and when they were issued? 

Passed for a slew of reasons, but at least plots of land, compared to time of permitting, compared to all costs involved did compute for decent final rent roll.Bottom line is that when a rehab costs as much as your purchase price and you'll end up with same size and sq footage you started at...pretty much a never. 

In Minnesota I would prefer any heat other than electric, property located on a busy road, in a town that has a growing population, in a city that does not require a rental license or permits, updated electric, garages would be a plus.