NOW, if you had them in the series llc, all that they can sue under is that one series that the injury or lawsuit happened.

Perhaps look for properties with additional rooms to rent, or an ADU (in-law suite)...or room to build one that could offset this loss. 

The approaches used to own income-producing assets also have tax implications and lawsuit exposure.

After all this, make sure you file a lawsuit against the previous tenant and occupants to recover the rest of the damages.

Will I be likely to face lawsuits and liens related to the work done by the auction buyer and his contractors (the lien period won't close for a few months.) 

In this scenario, the lenders do not file a lawsuit but rather file this document directly not he land records to provide proper notice to the public that the lender is intending to sell the property, usually via a private trustee's sale.

Okay, I think under Texas law the landlord must give tenants 3-day notice to vacate before they can file for an eviction lawsuit.

A bigger section where my fiancé and I will live (after we get married in August) and a smaller in-law suite section.  

Asbestos...Of course the concern is tenants and law suits.

Putting your last name on your real estate LLC isn't going to help you at all during your first nuisance lawsuit.