Hi X-Himy. Thanks for stopping by my humble board. Interesting topic you've started here. I must agree that the old Fox episodes of the Batman animated series were superb. I hate the new ones on WB (the art is horrible now). I can honestly say that Batman was the best animated show based on a comic book that I've ever seen. I always loved the episode where that poor schmoe was screaming at the Joker before he knew who the Joker was, and the Joker kept tabs on the guy for years until he needed him to help with a crime. The guy acted like he was gonna blow up the Joker, but he had a fake bomb. That one was excellent. Not only was the art superb in the gold old days of Fox, but like you said, the music was awesome too.
As for your questions, a lot of the episodes were at least loosely based on actual comic storylines. For example, the ones with Ras Al Ghul that were on Cartoon Network last week were heavily based on a comic storyline. There were a lot of "original" storylines just for the show too though. The interesting thing though is the trend right now of the comics mimicing the animated show. The Harley Quinn and LockUp characters created for the show were added to the comics continuity. Also, They are designing Batman's costume and the Gotham City of the comics to look more like those of the newer episodes (unfortunately the WB ones). As for accurate interpretation of the character, I can't say. There have been too many different portrayals of Batman in the comics too judge that. However, I must say that as a comics fan, I felt it was about as fitting and well-done of a portrayal they could have done for the mass market. I loved the episodes on Fox, but I'm not too fond of ther new WB ones. I haven't really watched a whole lot of the Batman Beyond ones or the Superman shows, but I'm not overly fond of them (there were one or two excellently done Superman ones, including the big crossover with Batman one). The Fox ones were about the best animated comics shows I've ever seen.

-'Tamer