Yes, a stay at a Moderate or Deluxe resort is needed to get the Regular Dining Plan. A couple of years ago, when a Free Dining offer came out, the Dining Plan offered at the Moderates was the Quick Service Plan. If you wanted to upgrade to Regular Plan, you had to pay the difference. I've only seen that Moderate+QS FD offer that single time.
One other difference between a Paid Dining reservation and a Free Dining reservation is the minimum ticket purchase required for each person in your room. For Paid Dining, it's a one-day basic ticket minimum. For Free Dining, it's a two-day basic ticket minimum.
If you book a Room-only reservation, that cannot be converted to a FD package reservation. Room-only and package reservations are two different booking systems on Disney computers. Your only choice is to cancel and re-book when going from one type of booking to the other. BUT, if you book a Paid Dining package now, you could modify that to a FD package, since they are both packages. I did this exact thing 2 years ago. You have to be ready to re-book as soon as a FD offer appears -- types and number of rooms are limited.