You can call the police and have them thrown out on their butts.

I did not do any NACA activities prior to closing and I have not been asked to do any as of yet per the requirement (there are no NACA police to constantly check on you that I know of so alot of these actions are in good faith from what I have experienced). 

Post no trespassing and keep a deed handy to show the trespasser and the police.

New Orleans Police Dep’t.

I again asked my tenant if they might have done this on accident before going to police and starting a fraud investigation and then they remembered now that they received a check that they thought was for a return of taxes they were waiting on. 

More details/example fees: Management Fee: 10% of gross rent collected, $50 minimum per unit.Leasing: One full month’s rent upon execution of a leaseOther: 10% will be added to each invoice for any repairs, maintenance, improvements, landscaping, and snowremoval for the Property 50% of late fees collected $50 lease Renewal Fee $50 per utility turn on $25 posting 3 day notice $100 per court appearance witness fee $50 tenant removal with bailiff or police $50 to meet inspectors for housing voucher programs, occupancy certifications, and/or POS or rentalinspections Broker may charge to offset Broker expenses for postage, key copies and other misc. expenses $100 set up fee $120 annual consortium fee ($60 March 1st, $60 Sept 1St)Given all this, how do I input it when I'm making calculations for a potential investment (do I put this in as >10% like 12%, 15% or 20%?

Police deal with criminal matters not civil. 

Domestic abuse police arrests ( at least 2x monthly)3.

Already called the police and they successfully removed him and I secured the property but im concerned that he keeps showing up when the unit is ready to resale/rent. 

@Kristin Vegas - If you are buying in Chicago proper, be sure to become familiar with the landlord tenant ordinance which is specific to the city. https://www.chicago.gov/city/en/depts/doh/provdrs/landlords/...There is a good stock of multifamily housing just west of the city if you are looking for a more suburban feel with better schools and policing while still being able to get to the Chicago city center within 15-20 minutes.