We did our first two with 10% down no PMI through a local bank.

The bank may not allow this, im not sure.

As for your lender question, you'll probably hear a lot of people suggesting small local banks.

We would have bank statements, 401(k) statements, tax returns, etc. that would show our current assets.

The government can put a lien on your assets, and banks don't like to see that. 

I have never heard of a bank re-checking employment unless there’s an event that triggers it.

HELOCs aren't like 30YF first position mortgages where you can call 10 different lenders and all are within 0.25% to rate with very similar requirements.... each bank is making up whatever they want for the HELOC in terms of conditions, requirements, rates, etc. 

This means keeping the security deposit in a separate bank account, tenants depositing rent into a separate bank account, and having the ability to apply for a business credit card to charge house improvements and repairs to.

After leading us on for nearly 8 months, she finally informed us that the bank rejected her financing because the house is wooden and has a greater risk of being damaged by the tropical weather.Recently we were presented a cash offer of 75k and the house was appraised at 112k in November 2017.

You will have escrow fees and you will have loan fees which are paid to the bank if you're getting financing.