Seems you’re looking for appreciation with steady income and that’s a good approach in this current market state. 

2)  Do lenders typically allow cash out's ($247k seems like a big number) on blanket loans?

I notice a few comments from out of state lenders/brokers that are referencing what seems like the property taxes and/or transfer taxes, not mortgage recording tax.In NYC transactions, property taxes are pro-rated and sellers + buyers pay for the portion they're responsible for (depending on the calendar schedule of the county + closing date). 

This seems like a lot of work for a small payout.

My realtor did a walk through via FaceTime and the property seemed to be in great condition.

He eventually complied with my request but seems to have become incredibly bitter about it.

It seems like if I could put together 3-4 people who are interested in the same deal, and get them to pool their capital together on a flip, you would lower the per-person risk, you would allow more investors to enter the market. 

The numbers you are showing me it seems like you need funds to get it done and owe funds.

Although, Redfin estimates this property in the range of 269K to 320K so seems to be on the higher end of the bargain. 

The buyer-broker contract should specify the agent's duties of representing you, especially how they handle your funds, which seems the most serious thing you mentioned.