What is Alexandra doing there anyway? She's not a band member, she doesn't work for them, and she doesn't serve any useful purpose. She mainly causes trouble and throws herself at Alan. Why hasn't she been shipped home?
She was in the comics.
But so was Pepper, Valerie's predecessor, yet she's not in the cartoon. There's no in-story reason for Alexandra tagging along.
Maybe she's there because it would be too much trouble to make her quit following them around?
Why does Valerie play tambourine as opposed to, say, guitar or keyboards?
Presumably because every cartoon band of the time had a tambourine. The 2001 film at least had her be the bassist.