How to perspective employers check previous jobs if a company has gone out of buisness? -

Wonderful question, I m a banker and most of the places I worked at are no longer in existence.I guess they can google it to see if they really existed then take your word for it that you actually worked there.

I am in the process of opening a new small business in East Tennessee.? -

I had originally planned to operate it as sole proprietorship, because it was the easiest way to go. Now I am wondering if I should run it as an LLC or some other type of entity.

I would almost always recommend operating as an LLC. As a sole propreitorship, you are opening yourself up to unlimited liability. I work with entrepreneurs and investors exclusively on entity formation and asset protection strategies. If you need assistance, let me know.