So far I have been unhappy with what I have seen from this property management company and would like to terminate their management of these 2 properties when I purchase the homes.My dilemma is the leases are between the "ABC Property Management Company" and the tenants. 

There is no "Standard Lease" in Illinois.

Hello BP:I’ve been approached by a professional who would like to lease one of my apartments and utilize it for AirBnB.

So even if the average is $1050 that doesn't mean that houses also couldn't go for $1250 or $800 in the same area depending on its individual characteristics.3) It's not entirely clear where Rentometer pulls its data from, but I think they are using list prices instead of actual lease prices.

They've overflown because no one put the trash cans onto the curb.I could somehow try to get tenants to do it, could write it into leases, but I don't particularly want a bunch of $50 trash whodunnits.I have to imagine that many landlords just pay someone to put the trash cans onto the curb. 

On the original lease it listed the Husband, wife, and 3 kids.

What am I getting in if I purchase a *leased* property?

I guess you call it a sandwich lease but not an option (not to own). 

From those one looked fairly good, well managed on the upswing as a new owner had come in and started remodeling and kicking bad tenants out. 24 unit complexList 565,000Purchase Price 535,000Gross Rent:138,000Less Vacancy(10%) 13,830Operating Income 124,470Property Tax 8,837Insurance: 6,900Management(6% after vacancy): 7,468Maintenance(6%): 8,298CapEx(6%): 8,298Water: 8,400Waste: 2,700Electric: 8,400(laundry room, hot water heaters, security camera's)Cleaning(unit turnover): 1,800Landscaping: 600Operating Expenses : 60,301Net Operating : 64,169Loan Payments(100% financing): 42,369Cashflow:21,80024 units - 16 2bedroom and 8 - 1 bedroom lofts.

And unless  there is a lease you can raise the rent to what ever you want