The lease termination fee needs to be paid at the time they request this, do not substitute the security deposit for this purpose.This will ensure compensation for time, money and effort needed for a tenant turnover, including advertising and showing costs, regular repairs, utilities during vacancy etc.

To supplement my down payment, I have secured $50k via gift and inheritance.

I have heard mixed responses on whether to charge both first and last month’s rent and a security deposit, or just first or last month’s rent and security deposit.

It is no different than maintaining the electrical outlet for the W/D or the plumbing for the washer.  

Security Deposits / Escrow: If you would like to use Baselane for an escrow account, you can simply open another sub account that is separate from your day-to-day activities.

Let's say I buy at tax sale, I want your rehab money 30 days later, would you lend to me for the rehab without security of the property?

Security deposit amountYou can find plenty of examples by searching for "tenant estoppel certificate doc" or exchanging "doc" with "pdf" for more options.Here is an example and explanation: Sample EstoppelSome have a lot of legal jargon but this document does not need to be so detailed.

Borrowing from multiple investors on one note creates a security that likely requires a registration or some other form of exemption.

It is cheaper, easier and more secure. 

Give them 24 hours to pay the security deposit and sign the lease.