If you are purchasing in your name, you should be covered by your homeowner's or renter's policy which typically include liability coverage.

People always go with the first person that brings them a flip and then suffer loses.

One of the recent 'touches' we are going to add since we have the equipment at our 'day job' is to laminate the front and back covers and use a binding machine (total cost about $150 for them) instead of just stapling things. 

Ones under negotiation ask the seller to cover closing costs and raise your offering price to cover the closing costs.

Is there anything they should be covering?

It'd just be one less person to hold accountable if things go bad or they end up leaving damage/money owed that isn't covered by the security deposit when they move out. 

Additionally, what if I or a contractor had an accident and received bodily injury, would we be covered under the homeowners insurance policy?

I'm ready to start looking at properties and identifying a contractor/s I can work with, what type of insurance will I need to make sure my business is properly covered and does that have to be renewed/added to each house I flip or is there some sort of umbrella policy that I can add and remove properties as my business progresses?

Depending on the carrier this can be exclusive to Category 1 and above Hurricanes or it can also include Topical Storms and/or Tropical DepressionsTropical Cyclone - A little broader in that it will generally include any storms that originate from the Gulf of Mexico regardless of the status (hurricane, tropical storm, etc.)Wind and Hail - The broadest in that it not only covers any storms originating from the Gulf of Mexico but any wind and/or hail damage regardless of where it originated fromThe reason why you need to pay attention to this particular deductible is because it will be percentage based deductible; keep in mind that this means that if your cost of insurance on the dwelling increases, so does the deductible.

I would contend that if, as you say, the rent barely covers the mortgage, you will end up losing a lot more than that over time by holding onto the house.Repairs and maintenance on a house are not cheap, especially on one that is 100 years old.