Third edition says (on p.136), that a Horror Mark lasts for a year and a day, at which time the Horror may choose to renew it for another year and a day (and so on, and so on), if the character is in range for it to do so.
(It's worth noting that certain methods and components - such as cockatrice blood - are rumored to be effective Horror Mark removers, so slaying the Horror is not always necessary... according to these rumors.)
The Gamemaster's Guide (3E, p.274) has the following on the Horror Mark's effect on the marked character's artistic ability:
Determining if a character is under the influence of a Horror by
having him perform an Artisan skill is unlikely to result in real
proof — this widespread tradition is the result of centuries of legend
and superstition. However, that does not necessarily mean that this
method never works — some Horrors do pervert the Artisan skills of their
victims (...)
The book also emphasizes that the Horror Mark described by the RAW is practically just a template that gamemasters should twist and modify as they please - that is, to best match their stories.
I haven't found and don't remember having read more specific answers to your questions in the RAW. My answers would be:
Characters lose their ability to create art only if this suits the given Horror, and only when and for as long as the Horror wishes. If the Horror is slain, its specific, unique Horror Mark ceases to exist, therefore artistic abilities return. Consequently, I don't think the Horror must be slain by the specific character it marked for the mark to "dissolve."
Disclaimer: I haven't played ED for quite a while, and there's tons of material for the game that I'm not (or no longer) familiar with. The above relies just on the (3E) core and my memories. Other answers may have more solid info, based on a broader and more active knowledge. :)