2.) I think part of the problem is the writers just didn't know what to do with her. The character was essentially rebooted twice during the early years.
They started her off as sort of a wise-old-sage. They were trying for the ironic twist of Obi-wan in a young woman's body. That didn't work.
Next they put her in the strait-up science geek role, the go-to exposition person. Essentially, she was Spock lite. That didn't work either.
Finally they settled on the "free-spirit" thing. But they never felt comfortable with it and retreated back to a previous persona whenever they could. .
Bingo, except I thought the "free-spirit" thing worked better than the others. But, yeah, Jadzia had no consistent personality for the first season or so. (She got one eventually, IMHO.)
True story: when I co-wrote my one-and-only DS9 novel way back when, I just couldn't get a handle on the character and avoided writing about her as much as possible--to the extent that our editor complained and made us go back and add some more Jadzia to the book!