Currently my plan is to graduate, get a raise, save down payment, and finally purchase a property aiming for a reasonable cap rate and cash on cash return.

It is pretty much a role of the dice as to whether or not this type of contractor has solid insurance and I would be very diligent in making sure this type of contractor is properly covered and ask your agent to review the actual policy in addition to the certificate. 

From my searches it seems there are two types of policies - Rental and Landlord.  

I just have an umbrella policy with my insurance for my STR.On the insurance question, I believe you need to have the umbrella policy with the same company as your primary home owners insurance.

Yes, the builder's preferred lender has offered me this:"To do it, I had to go with a FHA loan, buy the interest rate down to 4.5%, and increase the down payment to 11%...we will pay the Owners Title Policy plus $2k towards the closing" costs."

It looks like some people are recommending to hold in your name and just have good insurance and possibly an umbrella policy.

At least as of a few months ago they didn't seem to have a hard policy in place across all markets, but maybe that's changed lately.I personally would find out or run a test with opendoor, make some connections and see what is plausible personally as it could depend on which market you're in, which rep you get etc. 

If you have concerns or risk factors there get an umbrella insurance policy to protect yourself. 

What I’m doing with my properties is I am getting the financing in my name, using an umbrella policy until I have paid off a property and will then transfer them into an LLC.

When you say that the title co sent you an amended report with this removed . . . did they list this as an exemption on your title insurance policy, or they removed any mention of the lien from the soon-to-be-ex?