In the book series "Warriors" by Erin Hunter, Brambleclaw does not kill Firestar. Firestar dies in battle against the Dark Forest warriors, sacrificing himself to save his clan. Brambleclaw later becomes the leader of ThunderClan.
Yes, Firestar and Brambleclaw are related. Firestar is Brambleclaw's father.
He kills him by using a part of the fox trap that was supposed to kill Firestar
Some people don't like Brambleclaw because of his relationship to Tigerstar and because he was tempted to kill Firestar. However, Brambleclaw did prove his loyalty when he killed Hawkfrost to save Firestar.
Brambleclaw kills his half-brother, Hawkfrost, in self-defense during a battle. Hawkfrost had betrayed ThunderClan and threatened Brambleclaw's life, forcing Brambleclaw to kill him to protect himself and his clanmates.
He and Brambleclaw were with Firestar, who was stuck in a fox trap, and Hawkfrost told Brambleclaw to tighten the trap and kill Firestar, but Brambleclaw killed Hawkfrost instead, fulfilling the prophecy "Before there is peace, blood will spill blood, and the lake will run red."
Haawkfrost died when Brambleclaw stabbed him in the stomach with a stick. This was when Hawkfrost trapped Firestar in a fox trap and was about to kill him when Brambleclaw stuck with loyalty and turned on Hawkfrost.
Firestar made Brambleclaw deputy because Leafpool had a sign from StarClan saying he was the right choice.
I think that Firestar would be proud, because Brambleclaw is a good and brave warrior.
Ashfur was the cat who helped Hawkfrost try to kill Firestar in the last book in The New Prophecy Series, Sunset. In the fifth book in The Power of Three Series, Long Shadows, Ashfur reveals himself to Squirrelflight, Jayfeather, Hollyleaf, and Lionblaze as the one who attempted the murder. He was furious at Squirrelflight and wanted her to feel the pain of losing a loved one like he when she left him to be with Brambleclaw.
He dies when Firestar gets stuck in a fox trap and he wants Brambleclaw to kill Firestar so he can be leader. Brambleclaw reacts to his leader instead. Next, Hawkfrost threatens to kill Brambleclaw. He thinks quickly and shakes up the pole from the fox trap. Letting this get tamperd, he grabs the sharp pole and right when Hawkfrost pounces, she nails it right into Hawkfrost's throat.
Firestar didn't die yet, but I'm gussing Brambleclaw
No, he'll die in the same battle as Firestar.