No, we would be bringing some money to the table for down payment, closing costs, etc.. 

If I am unable to change the financing structure due to high costs of refinancing, are there ways to still protect the assets under an LLC?

However it really depends on your credit score, LTV and cash flow of the potential property you are looking to purchase.

So FHA has two sections:FHA section 203(b) is intended for properties that are move-in ready.However, FHA section 203(K) enables homebuyers to finance the purchase of a home and the cost of its rehabilitation. 

(or their forward hedge. which also cost a lot of money) The market for mortgage backer securities sets mortgage rates not the lender.

Also, please bear in mind costs; some states could have annual fees for an LLC in the hundreds of dollars (e.g., California),  whilst other states have no such fees (Texas).

I'm potentially looking to purchase a small rental building which falls under the NYC rent stabilized program.

I am not as concerned with cost and would prefer quality and transparency.

Secondary is to raise potential rents for when I move out soon and rent it. 

A simple mistake can cost you more money or time.Here's a pretty good guide: https://www.clarkcountyohio.gov/DocumentCenter/View/5210/CCO...