I am a bit confused could you please elaborate further?
I have some questions:
Absolutely!
1) If we choose to claim the NFT of a physical artwork that we already hold, will we still keep the physical certificate of authenticity?
Yes. When you claim the NFT, the CofA becomes void. We will have a look-up tool on Cryptoat.com that allows people to check if a specific NFT has been claimed
" If you want to sell the art piece, you simply sell the NFT. "
2) If we claim the NFT, and then decide to sell the art, by "simply sell the NFT" (and deliberately keep the physical) who will be the "authenticated" owner of the artwork? The new NFT hodler OR the seller that still holds the physical artwork & the physical CoA?
The current NFT hodler. In fact, you are perfectly entitled to keep the physical. You just aren't entitled to sell it without the NFT.
3) In Cryptoart.com V1, "Selling your art piece requires physical delivery.".
In Cryptoart.com V2, selling your art piece does not require physical delivery (of the physical artwork)?
Nope. Just drop the NFT on Opensea or another marketplace. The new owner can then reprint or enjoy the art in any form they like. Think of it as form agnostic.
"and the art will be marked as such."
4) How exactly the "art will be marked as such"? Which art piece, the physical OR the NFT? How will the NFT distinguish itself, if the new owner received the physical artwork too? (to be marked as such)
The physical will be marked as "not for sale without the NFT provenance" on the back. Not sure I follow the last question, so feel free to rephrase if I didn't cover it.

"Physical art pieces created with the NFT are only for personal use."
5) What's the usage status for Physical art pieces created without the NFT ?
If you are the NFT owner, you can use them in any way as long is you don't sell physical or digital good commercially. i.e. dilute the supply.
If you have a physical good without the NFT, it is considered an invalid piece. Much like reproducing a copy of the Mona Lisa, you can keep it personally, but it won't have a secondary market value.
6) In "Cryptoart.com V2", you mention that "The authenticity will shift to the NFT". Does this mean that from now on, NFT will act as the CoA, hence it be provided instead of the physical certificate of authenticity (with every physical crypto art purchase)?
Going forward on new art pieces, yes. It doesn't affect selling V1 physical art pieces, except that the potential buyer will want to check our website (or etherscan.io) to make sure the NFT has not been claimed.
thank you in advance, and I wish you all the best. Looking forward to getting some NFT's for my current Cryptoart physicals....
You are welcome! These are great questions. This is why I posted here first. This will help with the FAQ and also help to align the message.
Best,
Troy