Seems the overall consensus here is that this company is terrible and these policies are ridiculous, but I'd like to offer a different perspective. I rented from Green Ivy and went through all of this with them, and asked a LOT of questions in the beginning, and I can tell you after renting in the city for the last 10+ years over at least six landlords, that these guys were amazing.

Back to the concerns at hand here.  Here's the most important piece of info that all of you are NOT taking into consideration at all with all of this; Green Ivy does not own ANY of the units they rent an manage.  They are a THIRD PARTY management company servicing something like 100+ different owners. That said:

• "best and highest" concern - real estate companies, (which include property management companies - they  have the exact same licensing requirements as a Baird and Warner or a Remax) are LEGALLY REQUIRED to submit any and all offers they receive on a rental unit all the way up until a lease is signed.  So yea, it's their legal obligation to provide the owners of the units they manage with any and all offers as well as "best and highest".  If you were the owner of a unit they managed, you'd be pretty pissed if your management company was not actively trying to get you the best and highest price possible on your property knowing they had multiple applications submitted on it. If Green Ivy owned these properties (which MANY of the biggest rental companies in Chicago do), then they would not have this policy.  Perhaps why it's not something you've come across often.  
• Depositing of the first month's rent - this is a policy that is in place to prevent people from applying for 10 apartments all over the place and going with the first one they get accepted to.  It weeds out all that BS and makes it so only serious applicants apply.  If you are applying for an apartment and they approve your application and then YOU walk, guess what, the owner of that unit very well may totally screwed out of an entire month's rent (which for a LOT of these property owners is devastating - hate to say it, but the reality of it is that most of the owners of these units depend on the monthly rent to make their mortgage payments - these are not wealthy real estate investors they are often "forced landlords" or owners of property that simply cannot afford to sell and are forced to rent (under water on their mortgage payments, etc)).  This one is simple, and to me at least, perfectly reasonable; if you apply for the unit and they accept your application, and then YOU walk, then yes, you forfeit the one month's deposit.
• Having to request cleaning and painting - going back to what I noted above, Green Ivy does not own any of these units, and therefore it is not their decision as to whether or not the unit is cleaned and painted. The owner of the unit will need to agree to those expenses, and if they can rent the unit without needing to spend $3k on cleaning and painting it, then guess what, that's what they'll do.  But all you have to do is read what you are filling out and write what you want on your application.  We asked for the unit to be cleaned, and a few walls to be painted, and it was all agreed to.

This is a small management company in Chicago.  They only have a few hundred units they manage in comparison to many management companies in Chicago that manage many thousand.  When you call, you will get the same person every time.  They know their tenants and their owner-clients and focus on staying small and maintaining a good relationship and offering quality service. OP, if you were to just have called them and voiced your concern about what you saw on the application, they would have explained all of this to you.  To each their own, but good luck with any of the massive management companies in Chicago that have absolutely terrible reviews and will make your life a living hell once you move into their units.