.- The guy bought the property in 2004 and it's been vacant for a couple years, but he has been checking in on it periodically.  

I upload documents on their portal, pay for the appraisal, wait for an indeterminate period of time; I close in an LLC, and don't have to show tax returns. 

Does a 5-day inspection period seem reasonable for a 2 to 3-unit property in Chicago?

Energy efficient, double pane windows cost way more than single pane retrofitted windows.

if so is there a time period say like a 3 months history of receipt of funds from these in order to use those as a source of income?

My opinion, during an inflationary period, real estate is a good place to invest.

The average hold period was 25 months, with the longest being 36 months.

She will most likely have to notify the landlord of the problem in writing, wait a specific period of time, then deposit rent into an escrow account. 

I've tried various things: shorter inspection time period (typically it's 10 days here, and if you do a 3 or 5 day inspection time you can be attractive b/c the seller can get it back on market quicker if you find something you don't like during inspection period); non-refundable earnest money (maybe $1000 of money that you will not get back for any reason on your side - not if the seller breaches-- should the offer not go to completion - this shows you are an extremely interested buyer, but you could lose the money, so use cautiously and with the advice of your agent who knows how to correctly write that into the contract); put a limit on the repair request no required by lender - cap it at $0/as-is, or $500; a higher earnest money - like $5000, shows you are serious.

Things that we have discussed are rights of refusal if either party wants to sell their position; a minimum hold period of 7 years, & only making withdrawals if there is 10k reserve in the shared account.