There is no minimum that needs to be injected by an investor. 

You must then inject another $500k for capital improvements.

The property I owe $1800 on is worth approximately $80K, so I have been looking into doing a cash out refi for a cash injection to help with the purchase of more properties, but I feel that the closing costs are excessive.My question is, is there such a thing as too much to pay in closing cost/prepaids for a refi or is it just the cost of doing business?

--Seller (is unknown) of the presence of an exterior injection well on the Property.

- Do their cash flow projections indicate that they will remain solvent or require additional capital injection at some point prior to profitability?

Leaving $70k on the table by not injecting $30k into the property seems a bit rash, but seller's do weird things.

A personality injection?

The bank is now telling me I can use any expense during this as part of my equity injection?

As long as it cash flows you leverage cash and still do good on the up cycle.If the bank wants big down then you have to really hammer them on a reduction to justify injecting precious capital.

As mentioned, you're in this one for the long term relying on appreciation and established equity.Looking at financial ratios, like cash on cash or ROI are rather meaningless with no cash injected and assuming debt.