No, but Prim does
When her father taught her to hunt in the woods, he would sing and the birds would fall silent. The mockingjays liked his voice and they would pick up his melody and repeat it. Katniss learns that the mockingjays, too, like her voice and the mockingjays remind her of her father. She treasures the mockingjay pin as she believes as long as she has it with her, a part of her deceased father will be with her, too.
Mockingjays remind her of her father, who used to take her hunting out in the woods. He would sing and the mockingjays would repeat his tune.
They decide to bird-whistle to each other through mockingjays
I have counted two. You have the lullaby that Katniss sung to Rue while she died and "The Hanging Tree", which Katniss sung in Mockingjay to Pollux and the mockingjays.
Annie's full name (Annie Cresta) was mentioned by Peeta after the incident with the mockingjays in Catching Fire, where the mockingjays imitated the screams of Prim, Gale and Annie to break Katniss and Finnick.
They use a 4 note whistle or melody, and the mockingjays in the forest carry their signal to the other because the mockingjays tweet melodies to each other and it gets carried on. Their four note melody means that they are safe.
jabberjays mated with mocking birds and started own race of mockingjays. katniss has a mockingjay pins she wears with her during the games. audience saw it and associated it with katniss. it became her talisman.
SPOILERS: no she does not die she marries peeta at the end of the book
No Katniss marries Peeta and live happilly ever after and Gale tries to marry Katniss.
they are related because Prim is the sister of Katniss
Whistling, so that the Mockingjays would hear, and then distribute the call throughout the woods.
the government used to make birds called jabberjays that picked up peoples' conversations and sent them back to the capitol. they were used to find traitors and people conspiring against the government. people found out about these, though, and began to feed jabberjays useless or false information, so the government abandoned the project. they left the jabberjays where they were to die out, but instead they bred with mockingbirds, creating mockingjays. mockingjays can't mimic words, like jabberjays, but they can repeat a tune if they like it enough. katniss' dad had such a beautiful voice that the mockingjays would take up a song whenever he sang it. (that's why mockingjays remind her of her dad) THE mockingjay, however, in later books, is katniss. she has a pin she got in the first book with a mockingjay on it, a symbol of defiance, and she wore it continuously in the first book. people call her the mockingjay in later books, because of her pin.