Shrennin
Didn't get the memo regarding the 14th Amendment
Yes, but there are no bigger stories in Batman TAS at least. I have a spotty memory of Beyond, but I think there wasn't a storyline either. Continuity isn't the same as an overarching plot, the single episode stories are self contained and don't add up to anything, in contrast to ATLA where everything, even "filler" episodes worked in context of the bigger story that went from the first episode to the last.
JLU did more of that. The Cadmus arc in particular was amazing. I don't remember too much about Batman Beyond in particular -- the Batman Beyond finale aired in JLU which is why I remember that episode so well. It's hard to have one specific storyline for a superhero show (like Avatar) so I guess if you mean in the context of working up to a big finale then I guess you would be right but I think the show is more how the heroes evolved over the course of the entire series of cartoons during their many battles. It's still not like most cartoons where the events of the story don't affect the characters in it. Granted, some episodes are completely one-offs, but others aren't (at least in terms of character development).