"Art is free!"
I'm not sure what we mean here by using Вільне. Does it not say art is free/available? Sound odds to me because I think безкоштовне means without cost. It's not clear what the course creators have in mind here.
I think it means that art is not bound by dogmas or something like this.
Yes, but it's a neuter noun and not masculine, so make sure you use the neuter adjective endings: Мистецтво безкоштовне.