instead of anxiety we could use the word "worry"?
I'm coming around to the word "rumination."
Although "worry" could work for future directed anxiety.
should everyone try to live a worry-free life? Is it even possible? Would a worry-free life be worth living?
Yes to all, in my opinion. It comes down to whether one can take action or not. It seems similar to the sentiment encapsulated in that Serenity Prayer. Basically, if something can be done about a situation, do it. If nothing can be done, don't worry about it. Make prudent decisions about both.
Should questions like these remain a personal exploration, so there is no right or wrong or absolute answer that applies to everyone or to every time and place? Or is this a help line of discussion amongst friends?
It seems to me that Epicurus was fairly clear and firm that ataraxia was a necessary component of a pleasurable life. It's not morally right or wrong, it's a way of experiencing our lives, clear-eyed, worry-free, and taking prudent action in all situations that will lead to the most pleasurable life possible for ourselves.
PS: And I speak as a "recovering ruminator" myself!