Are there any special offer for trademark owners?

Yes.
Individuals and businesses in possession of trademark names may qualify for significant discounts on .art domain names. Please fill in the contact form here to see if you qualify.

I own mywebsitename.it. Do I have a priority in obtaining mywebsitename.art?

No.
Owning the equivalent of the domain in a different top-level domain does not, on its own, give you priority. If you want to secure the .ART domain, the best is to purchase the desired .art domain sooner than later to avoid it being registered by someone else.