No*. You'll need access to a cassette tool and a chain whip, but it should be a direct replacement. At most you'd need to slightly adjust the gear indexing to account for any sprocket offset variation.

*Unless they're worn, in which case it would make sense to do them, and a new chain, at the same time.

No.

Changing a cassette is pretty trivial.
The only time you might expect to need to change the chain (aside from wear) is if you change to a bigger cassette and your existing chain is a bit too short leaving insufficient slack for the largest sprocket. Since you're moving down in size, not up you'll have no problem.
If your chain is heading towards it's wear limit you might consider changing it now too, as a stretched chain can increase wear on the new cassette. If it's still in good shape, just swap cassettes.

I've always treated a chain and cassette as linked consumables. Many shops sell them in a discounted bundle - worth taking advantage of that when you can find it. I also tend to drop down a level for these consumables e.g. I use Ultra Di2, so tend to use 105 cassettes and chains, unless I find a bargain sale price.

To the OP - download the dealer manual for the rear mech if you're worried about adjustment. It's fairly easy to adjust even for the novice and there are always the ubiquitous YouTube tutorials to watch too.

If you really insist to move to a Dura-Ace cassette (why??), I would def. change the chain just in case (unless you're very certain regarding chain-wear...)
Chainrings are usually ok, unless you rode with a very worn chain for some time
You might also start with alternating 2-chains, just use a quick-link on them and change every month/1000km or so; this will reduce wear on your new cassette and chain-rings

Cassettes are super easy to change. I change them often. I have about four I pick from depending on where I riding or racing. Add that to the cassette changes for my junior racers (and the weird requirements for junior gearing in some events but not others) and you find yourself changing them often. No need to change chains if they aren't worn beyond limits. I rotate three chains between my primary bikes

Thanks, everyone for the suggestion.
I change to Dura Ace since there is nothing else I can do with my bike :).
Mine old one is Ultegra 6700, so quite old.
Harry