Is this salt packaged in a peanut and nut free facility?

Yes, our Himalayan pink salt is packaged in a nut free facility

Exactly how fine is the grind??.. is it like typically available sea salt??

It's very fine, on the order of typical table salt. It is not like sea salt which is much coarser.

Does it contain anti caking agent?

Do not waste your money on this brand. When it arrived it was just a pink table salt. It looked nothing like the product shown in the picture. The granules are super fine. There is no anti-caking agent that I could tell. I was simply annoyed that the picture on the package was misrepresenting the actual product.