What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

No, you cannot use your VA eligibility to bid on a home at a foreclosure sale in New York.Once the sale has occurred, if the property reverts back to the lender (Meaning it didn't' sell to a 3rd party), then yes, you can use your VA eligibility to purchase, if the seller (Bank/servicer/credit union, etc.) accepts your offer, and, if the property meets VA requirements (Section 1, etc.).I sell the REO my bank takes back and I don't like VA because they try to stick me with fees and try to make me do repairs that we just aren't going to do.

I just looked online and they have plenty at Lowes.

That question will require an essay to answer every part of your question :) With stocks, you mostly gamble on appreciation.

My thought process is to purchase the property initially under my name so that we can pay 5% down as my understanding is that mortgages to LLCs are more difficult to find, have higher interest rates, and require a higher down payment (around 25%).

The requirement is that you live in it for 12 months if I'm not mistaken. 

Right now, all you are doing is book research or online research, so you need to put these random thoughts into the real world.

That said, I wonder if these are the kind of cameras that require "altering the property" in any way, because there is typically a provision in lease agreements that prohibits the tenant from altering the property without landlord permission. 

Of course, with all things, the answers to all these matters will depend on the circumstances.California tends to have more laws on the books and requirements and restrictions that it can be a good idea to form a CA LLC for out of state property so that you as a CA resident are covered, and to try to have your contracts fall under the purview of CA courts.

3. requiring heavy amount of rehab (siding, foundation, roof, HVAC, appliances)?