Install carpet in the attic

Technically, yes you can, but in reality the results might not be great:

1. Carpet is measured and cut to fit a house's floorplan: individual pieces are cut from a carpet roll to fit around the tricky bits in your house (door openings, inside closets, etc.) and then taped and ironed together on site. Unless you have the exact same floorplan, you're going to have some scrap, meaning it will have to come from a bigger house so that you have enough to fit yours¹.

2. Removing carpet without damaging it can be tricky. Think about your house's floorplan, and how you'd roll up a single piece of carpet to get it out your front door. Finding the seams between pieces is difficult because the original installers are trained to join separate pieces invisibly.

3. Carpet has a grain, so pieces cut lengthwise from a roll will look funny next to pieces cut crosswise.

4. The carpet gets a different amount of wear and tear in different parts of the house; if you have to join pieces from different rooms in the original house, they may not have worn the same. This may not be an issue if the house you're taking it from is new.

5. Cutting carpet is somewhat demanding. Installing carpet, even with a power kicker, is a job for the young and indestructible.

6. Carpet can pick up surprising amounts of dirt; be sure to have it thoroughly cleaned before installation, especially if the original owners have pets.

^1. I helped someone do exactly this several years ago; the carpet and pad came from an approx. 2000 sq.ft. house and he installed it in his 1000 sq.ft. basement. The house it came from was very open-plan, with large living and family rooms and three good sized bedrooms. After cutting pieces down to size to fit his basement rooms (1 large bedroom, 1 small bedroom and a living room), he didn't have a whole lot of carpet left over.

You will not create a problem of moisture in or on the ductwork. The duct work is insulated to keep the condensate from forming on the outside of the pipes and dripping off from the temperature differences in the attic in the summertime with AC running. So more would help. What would be bad is if the duct work is flex duct and gets mashed under the weight of the added insulation on top of it. Don't underestimate what will happen once you cover it up and can't see have may have happened to it.

About the existing decking, I feel storage is valuable in any part of the home. To cover it up and lose what may be valuable space, at least in my mind seems a shame. But if you are not using it, and don't plan on it, then there really needs to be no concern.. If that is the case then insulation added anywhere in a continuous layer is a benefit. I would if it were me, pull it up and set 2X10 material on its edge and screw it to the joists so the new insulation could run tightly between the 2X material, then add plywood over that, ripping it 2 ft. wide if need be to get it through the access.