This is how it is supposed to be handled but some lenders have overlays or loan officers are not aware of the actual guide lines or rules depending on their organization or who they are selling the loan to in the correspondence channel.I have come accross this several times you simply make the underwriter aware and in some cases the agents and appraiser are informed as well in case there is a need for an outside LOE letter of explanation. 

So any appraiser will tell you to prioritize location, usually 1-2 miles max and ideally under 3-6 months.

The price of the property was perfect and it has already appraised higher since purchasing.

Lets say current appraised value is 170k.  

Is 43% that insane if they 1) got the 16 homes for 400k when It was 600k ask from an senior that didn’t want to deal with them anymore and 2) and the apt appraised 200k over 3) 6 air bnbs bring higher return coupled with the 18plex

You'll wind up paying for an appraisal, maybe 600 - 750, and then when it comes back the lender will tell you there's no deal, the ARV is too low or you paid 100k for it but the as-is came in only at 80k so that's the number they are willing to lend you on, in other words this deal just got 20K more capital intensive for you and maybe priced you out. 

No idea about park appraisal once I go down that route for pads and pad rent I may be getting it totally wrong on how the bank thinks and appraisals.

Commercial lender will lend for a max of 15 years and up to 80 percent of cost, note UPB, and house appraised value.

I would also say that markets like Manhattan are not super representative of most markets in the US - a lot of foreign investment I'd imagine in NYC, Miami etc - I'd guess a lot of these cash purchases are more about exchanging unstable or risky foreign assets/currencies for perceived stability/safety of US top metro residential real estateI think in a lot of other markets where this isn't relevant - I think most are cash offers being "king" as not having appraisal or other contingencies that might sabotage the sale after 30 days or so and make people re-list (sellers will take less to avoid this risk and downside)

You can cash out in 3 months using the new appraised value with a DSCR loan.