It's a local bank in NJ, Gibraltar.

After researching online the steps bank takes to foreclose, I'm wondering if they've filed a notice of default.

A short sale makes things tougher, generally the owner has no money (which is why it is selling less than they owe) and I will just about guarantee the bank is going to say "no" if you even get a response.

What if I was Wells Fargo or some big bank...what would they do ?

That's why if you ever see a REO contract (bank owned), it will almost always state "non assignable".  

Many of the "big" banks don't like to go over 4 loans with one person, but there are plenty of mortgage lenders that will go up to 10.

You run it as is and bank the extra cash for the conversion when it gets reported.

If the loan amount is large enough it may qualify for Freddie Mac or Fannie Mae agency debt or contact your local\regional bank for loan products.2) Ask the listing broker if they can provide a submarket report from ALN, CoStar, or YardiMatrix. 

I would imagine they'll want to see some financial docs/bank statements.

I asked the bank if they could do in-house financing and they said YES, and could do a portfolio loan.