For a typical Saturday morning Bar mitzvah, a man would wear a suit and tie, and woman would wear a dress, or dressy clothing.
The Bar/Bat Mizvah.
A Bat Mitzvah girl can wear appropriate formal wear, such as an elegant dress or a pant-suit.
They may wear a kippah.
a dress
Wear your best, dressy clothes.
Bat bags are a type of purse that can be an accessory to your costume. I do not believe you can actually wear the bag as a full costume. If you wanted to use this purse it would be a great addition with a black dress and bat wings.
NO
Yes, the idea is to dress nicely!
The Bar Mitzvah is said to have matured and become a man. He is more responsible and reliable.
any
There is no specific colour worn by the bat mitzvah girl for the ceremony celebrating her becoming a bat mitzvah. Any nice outfit that she likes and feels comfortable in is suitable.
Girls wear a nice dress (semi-formal) or suit to her bat mitzvah ceremony. There is no symbolism. Some girls will wear a kippa (symbolises that HaShem is always above us) and tallit (prayer shawl) if it's a Saturday morning service where they read directly from the Torah.