Granted one has a great credit history and a sum sufficient for a down payment. 

If each of us signs title on a property is that sufficient protection or would an LLC be more beneficial?

To refinance do the lenders look at my income or rental income is sufficient to qualify for loan? 

At best if you financially qualify for a conventional loan from a traditional lender,you can get an FHA loan with 3.5 percent down if you live in it with the tenants.You will need a good job and good credit with sufficient income to qualify for that loan.Otherwise,you're looking at hard money loans with 20%or 30% down and several points upfront and a higher interest rate around 7% for a minimum of two years before you can refinance to prove you can manage the loans and make payments without problems.That's how professional investors do it normally.

You would do well to request a copy of probate "Letters" to review for powers.If full powers, a (15) calendar day notice of sale is sufficient, unless an objection by claimants, creditors or heirs.If limited or special powers, court confirmation is required and may be subject to overbid.

If you cannot get a sufficient appraisal or qualify for the re-fi, you would be foreclosed on...the seller may ever insert that you would quit claim the property back...there are a lot of moving parts on this...

Most probate properties are not the kind of deals with sufficient margins for a quick turn.

A relative may be sufficiently motivated to work with you.It may be that a formal Conservatorship has been established.

As you mentioned, quantity is the answer.  

In the case of cash offers, proof of funds may be sufficient for the purposes of making an offer.