This is a very good question. And a hard one too, which is probably why no one has replied yet.
Yes, I would say that the picture painted on the pottery of the Indian would be considered “a work of art”, primarily because it is signed.
As for the legality of photographing works of art, in a nutshell, if the work of art is in the public domain you are free to duplicate it however you want. If not, you could be breaking copyright law. In general, art becomes public domain after 70 years after the death of the artist.
For work that is not signed or you’re unsure if it is actually considered “a work of art”, how you decide to use the photo might make a difference. If it’s for personal use, you might be able to get by with more than if you were using it for commercial use.
These links you might find helpful: https://www.teachingcopyright.org/handout/public-domain-faq.html, https://bucks.blogs.nytimes.com/2010/09/21/when-its-illegal-to-photograph-artwork/
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