Can I just ask the listing agent for the "trailing twelve" or is that not allowed to do?

Regardless, I would get a paper trail going and if nothing forms within 7-14 days go to an attorney to get the ball going; your attorney fees can be spread through the other homeowners so don't be afraid to spend a little money; like another post said, you MUST protect your investment.

Although during the termite inspection they found old trails in the garage with minor damage.

It's very remote (I think only 50 cabins up there) and it has tons of hiking trails and a stream right out your front door.

I am on the trail of my first deal - I know it will happen !

Ask for the Rent Roll and the Trailing 12 Income & Expense report, then see what your NOI looks like.

I come from a family of investors who is trying to blaze a trail on my own.  

You are correct that it doesn't scale if you get employees but it's because of audit trails and controls and employee taxes. 

If I'm analyzing deals on multi's, should I expect to get the trailing-12 and rent rolls before I make an offer, or do I review those during the due-diligence period?

In Illinois, generally speaking, tenant can get a second appearance almost every time and on the second appearance, they could demand a jury trail.