1. Is this a first edition, first printing of the export edition?

Yes

2. Based on the photos, does it look like a cloth or paper binding? I tried to feel and compare with other books, but I basically know nothing about what the difference in look and feel is. I now see that the photo fo the front of the book looks grey, but it is more like dark blue. I only had weak yellow light on in the room. Can try to take a better photo if needed.

Navy blue cloth

3. If it is cloth + dyed top, does this make it a first state (or variant 1 as listed in Trotter's post on UK First Editions)?

It’s the first variant in Trotter ‘s article.

4. What exactly is a "headband"?

The decorative blue ribbon on the top. Which makes it “look” like a sewn binding.

5. Is there anything that looks odd with this copy? Something that might make us question authenticity? Besides the the spine being very faded, the dustjacket seems unrealistically good shape and the book paper is much thicker than what I would have expected compared with modern books. Do all later dustjackets have price printed on the front flap? Or is it possible that someone has discarded the original and put on a later dustjacket in better shape? How would I know?

No. It looks right to me. Later impression dustwrappers do have the price from what I know.

Thank you so much for the answers Foxrook! :)

Anytime! Hope it helps

As general advice on buying 1st UK Silmarillions, I'd generally say only buy copies without faded spines. These books are so incredibly plentiful that there is really no reason to pay a lot of money or accept anything less than a nice unfaded spine, so long as you don't mind waiting a week or two for the copies on sale to cycle such that there is a suitable copy. In the future when Tolkien is back to normal popularity levels, the only copies that are likely to be saleable are ones that are in very close to new condition. The sheer number of flawed copies available is mind-bending (unsurprising, given it was the biggest print run in the UK, ever, back in 1977)!

EmilK wrote:

4. What exactly is a "headband"?

Most of your other questions have been answered, but I think headbands can be expanded upon. Most of them are mass-produced and stuck on the spine today, but if you use a bookbinder to rebind a book then it will hopefully be done the traditional way. They are also called endbands as they can be at the top and bottom of the spine.

Trotter wrote:

EmilK wrote:

4. What exactly is a "headband"?

Most of your other questions have been answered, but I think headbands can be expanded upon. Most of them are mass-produced and stuck on the spine today, but if you use a bookbinder to rebind a book then it will hopefully be done the traditional way. They are also called endbands as they can be at the top and bottom of the spine.

That was pure, beautiful artwork.