Recently, they outlawed short term rentals of secondary dwellings.

Yes, FHA products can be used for 1-4 unit dwellings as long as you intend to live there as a primary residence for 1 year minimum.

This is the DE wording in 4603(b)(3), the Delaware Fair Housing Act: (3) To make, print or publish, or cause to be made, printed or published any notice, statement or advertisement, with respect to the sale or rental of a dwelling that indicates any preference, limitation or discrimination based on race, color, national origin, religion, creed, sex, marital status, familial status, source of income, age, sexual orientation, gender identity or disability, or an intention to make any such preference, limitation or discrimination.

By the way, instead of a duplex, you might be able to find a single-family home with an accessory dwelling unit to use as a rental.

I have really no experience in real estate, but I have envisioned myself getting into smaller buy and holds (single families or small dwellings). 

House hacking financials get significantly stronger as you increase the bed count above 4, or add a ADU or separate dwelling unit.

Depending on the Company for the current Homeowners policy you probably will have to rewrite the coverage to a Dwelling/Fire (aka Landlord) policy. 

We weren't registered with hpd (private dwelling). 

Your policy may say that any coverage is excluded for and dwelling or addition that does not meet code requirements.

Don't spend too much time dwelling on the "unknown" and prepare for the what-if's.