Medical Payments (A "good faith" payment, not subject to deductible that the ins. co. could make in order to avoid a lawsuit...if you do not have this limit in your coverage, don't fret.

If someone's going to file a lawsuit, its likely they're angry and upset, whether the reason is valid or not, its likely at that point, they're looking to get every penny they can out of you. 

The only criteria I had was to look at any single-family house that had a back house/studio apartment/mother-in-law suite or anything like that.

There is a lot of uncertainty whether DPP will have the registration in place by Oct 23rd, and if they don't, what will happen then but more lawsuits against the bill wouldn't surprise me.  

We would like something else, probably 1 million to start, that would help protect us from other potential lawsuits (unlawful evictions, injury, death, etc)I’m unsure which type of policy would be best to blanket cover our on LLC and would allow us to increase our coverage as the portfolio of properties increase.

Nobody and no entity are immune from a lawsuit. 

I am currently looking to get into house hacking finding a duplex, triplex or quadplex, possibly even a single family property that I could add a mother in law suit.

You can file waht is called a specific performance lawsuit.

Legal and equitable title also arises in trust.Quiet Title – An action to quiet title is a lawsuit brought in a court having jurisdiction over land disputes, in order to establish a party's title to real property against anyone and everyone, and thus "quiet" any challenges or claims to the title.

Most likely the state where the property is located is where lawsuits would be brought if they are something for personal injury like a trip and fall or something of that nature because the “cause of action” arose in that state.