Okay, so you specifically want arbitrage instead of to purchase something?  

And the IRS requires that all of the proceeds from the sale be used in the purchase of their new property. 

I would try to do 80% purchase loans on both.So 70k*80% = 56k loan amount 14k down payment + you will also have closing coststhen 120k*80 = 96k loan amount and 24k down payment + your closing costs So you will have about 32k - closing cost and loan costs for an additional investment

There is some purchase transactions and still private work (as I noted above). 

Hi, I am new to tax liens, how can I find them to buy in NYC? Do lists exist? Auctions?

We are purchasing a 6 unit Apartment building in a small central Texas town. 

How can I get an FHA Loan for an auctioned home when FHA Loan requires an inspector to come check out the building and auctioned homes generally don't allow for people to inspect the house until after purchase? 

Your ARV on something like that would have a much larger appreciation plus higher potential rents.If you purchased in the next 6 months it would put you in the early stages on the local market analysis. 

Is that the notice of Purchase and Sale agreement?

Because if your house hacking I recommend you purchase a 3 bed, 2 bath, 2 car garage.