I'm not used to dealing with roaches, but if you paid a company to treat it, there should be some sort of warranty for a period of time. 

I would likely treat the duplex as a long-term investment, focus on the cash flow, and disregard the fact that it's supposedly worth less than what I paid for it.

I mean to treat this purely as an investment property and will bite the bullet of living in a property for a year.

You have to treat everything with a business mindset.

. -- Lastly, does anyone have any insight on how lenders are currently treating individuals who have been out of work and have lower reported income due to covid?

The payments received by the seller over time are still taxable to the seller as long-term gain (though the seller may want to consider possible changes to how the feds treat gains taxes in coming years). 

Even if you go the owner finance route, they can still pull your credit and treat you as if you were trying to get traditional financing.

You may decide to carve out some cash to pay a bill or treat yourself or honor the gift. 

And every state will be a little different in terms of how you treat the deposit.

Reference 10/16/2016: https://www.housingwire.com/articles/38635-trump-treasury-pick-fannie-mae-and-freddie-mac-will-be-privatized/In mid December 2020, as detailed in this article entitled Mnuchin Rules Out Freeing Fannie-Freddie Before Biden Takes Over, it became clearer that the destruction of the US housing finance market would not happen and IMO the treat of a 'scorched earth' policy (at least for the housing finance industry) was averted.