Q.Daffodils
22 yrs ago I bought a property that had a lot of in-ground daffodils. I moved a few to other areas. After the first couple years, they kept sprouting and blooming. Then after approx 7 yrs into this, I read about popping the seed heads and/or pulling the stem that had the seed along with the seed. I pulled and popped a few dozen that year ’98/99. Ever since then I’ve been blessed or cursed with more and more flower heads that, for lack of a better term, look like they’ve exploded.
They resemble a geranium and last 3 days before turning brown and withering away with no seed heads just a hollow tube of a stem. This year over half of my blooms look like that. Someone suggested I had double daffodils but they in no way resemble any of the photos I see of doubles.

Unfertilized daffodil flowers do not produce any seeds. Behind the blossom there is a seed pod that will swell and populate with seeds when pollinated.
When you deadhead it makes for a healthier bulb which makes for better blooms. I have to agree with the assessment you were given about these being double daffodils. It sort of looks almost carnation-like, like the one in this photo: http://ih3.redbubble.net/image.9819849.9654/flat,800x800,070,f.jpg