Depending on a couple factors, you can certainly get better terms than 14/4.  

If I begin flipping, what possible issues could I be potentially exposing myself to that insurance may not protect me from and are these issues something that should concern me or are they low probability issues?

Over time, as you get exposed to more circumstances and situations your judgement should improve and you should rely less on the 'rules'.

Deciding factor will likely be cash flow. 

Will or no will, high value or low value, multiple heirs or a single child, mortgages or no debts, all these things will be factors in determining the complexity of the case.Since you'll need to know the next of kin (either directly or obtained from death certificate) you'll also need to think through what you'd say to someone who just lost a close relative. 

If you paid off your primary residence you would expose yourself to the same thing , no mortgage interest, But it would Not be profit. 

The key factors here are experience (and how well that experience transfers to the property / business structure in question) and relationships.Using myself as an example, I currently own and operate 6 SFR townhomes.

There's many more factors to consider than simply purchase price and rents.

The novelty factor could be a plus in an Airbnb situation though.

The quality of the neighborhood and what's on the market will be the largest driving factors when the appraiser analyzes your home.