Be upfront about your offer.Appraisals are an opinion of value at a moment in time.

Of course, 2 days later, the news comes out that Zillow has stopped their offers, so we made it just in time.

Honestly I'm blown away and slightly intimated by the amount of info there is available to us.

Buying houses and putting thugs and gangsters and cartels in, isn't a pleasant way to spend your time or money.

Go work for a brokerage with a broker who sits in the office and help two friends with transactions before you do surgery on yourself.Get a VA preapproval from an actual Underwriter and stick to under that sales priceCommon Mistakes that come to mind based on what you said:choosing a property that doesn't meet VA standards and losing your EMDfilling out the contracts wrong and getting suednot understanding inspection or appraisal notes and not cancelling the deal before the contingency date, lose the EMD and maybe get suedappraisal comes in low and not knowing how to arbitrate and negotiate, not having compssigning something without understanding the future resultsstating something false in writingsaying something that crosses Fair Housing lawsgetting the numbers wrong, not being able to get insurance in CA, offering on higher price than you qualify for...being busy at day job and not opening emails in time

You traded rent money for discomfort, and now the renter wants to haggle you for the amount.If it were mine I would have not traded discomfort for money, I want the money, and want to provide a "pleasant" Rental Experience as much as possible.Given that, I would have had a working window A/C installed as soon as possible after learning that the the existing one could not be fixed within a few hours.I would have picked one up from Home Depot that was less than 15 amps and provided a lot of cooling power--just one--but one that worked.As far as the repair, I would have updated the customer (renter) on the repair status as things changed.I would not have cut the rent--even if it was the cheaper way to go.

At this point in time you could try and buy it but need to pay off both liens but not sure if they have authority to sell it as it needs to go through probate unless of a trust

However, this occurred in times of FALLING interest rates.  

Buying and managing well, over time, tends to overcome any small errors in timing and/or errors in paying a bit too much.

If they can't sell, or sell in time, then the lender has to foreclose which is expensive.