@James Nix it looks like a metal sink with drain, but is different than the types I have normally seen.

Then there is the plumbing for the drain $50 some tile that needed to be replaced , grout , caulk , some lumber .

The fixture could have been $300 and all of your supplies and drain needed to be replaced....or not. 

And, after that experience, a process was put in place to ensure that all tenants sign-off on the initial walk-through checklist, that all repair requests have to be submitted by email with photos, and a "tool box" is provided that contains a plunger, hair removal comb for bathtub/shower drains, instructions on how to reset the garbage disposal, etc.  

It is likely that the backyard would need some grading so that water drains properly. 

Anyone can recommend a reliable plumber in Avondale/Logan Square to help with (hopefully) some minor things (slow bathtub drain, few leaks) etc. 

I have dealt with some pretty rough homes but always stayed away from ones with cement poured down the drains.  

That makes sense, I just don’t want to drain all reserves I have and put myself in a trick bag for my primary residence, I like to keep an emergency fund.

At my own home I do early routine cleaning and maintenance which runs about 100$ a year, so wondering if this can be done every 6 months or every year to clean the drain pan, filter, etc. at what frequency? 

Homes for yourself tend to be asset drains.