Etc) We have a corporation that we will pump the rent rolls through, so once the corporation gets off its feet, we have to get creative until we can purchase properties through it.

This means that you will probably need to pay registration and filing fees in at least 2 states if you don’t buy CA property as a CA resident.Any lawsuits should be limited to the assets of the LLC and not your personal assets (assuming you run the LLC appropriately and the corporate veil is not pierced, some debate as to SMLLC).

Keeping an LLC compliant so not to allow “piercing” of the entity is 90% easier than with a corporation.  

If you set up an S corp or LLC, you DON'T have to file a return.  

If we do all of the banking in LLC1's name, would listing the PERSON that owns LLC2 as an authorized signer pierce the corporate veil?

There is an abundance of supply, high price tag, it's more of a corporate travel town than a vacation destination (meaning that 1-2 bedroom units are in most demand, which puts you squarely in competition with hotels). 

I did it myself in AZ through  AZ Corporation Commission here in AZ.

For Euclid you must have a local PM : Per E.C.O. 1761.02(b)(2), if Owner/Corporation resides outside of Ohio, Owner/Corporation must provide alocal manager who resides in or has a place of business in Ohio.

Any corporation (IMB, Google, Automotive or etc) building anything in Louisville?

SMLLC is considered a disregarded entity unless you made the election to be taxed as a corporation(C or S)