It depends on which time. There are two main times that I can remember: in the New Prophecy set, Brambleclaw is mad that Squirrelflight took a liking to Ashfur instead of Brambleclaw. In the Omen of the Stars set, he is mad at her for lying to him about Hollyleaf, Lionblaze, and Jayfeather being his kits when they weren't.
It is unknown. I think that, even though Brambleclaw now hates Squirrelflight, they are still technically mates, whethere they like it or not. I think Brambeclaw would feel betrayed, but i think he still loves Squirrelflight deep down.
I don't think so
Because she lied to him about Hollyleaf, Jayfeather and Lionblaze being their kits.
Ashfur was mad at Squirrelflight for choosing Brambleclaw over him and he wanted revenge.
Because Squirrelflight chose Brambleclaw over him. In other words, he was driven mad by grief.
Yes, When Brmbleclaw found out that Squirrelflight lied to him, he was extreamly mad at her. In the newest book (The Forth Apprentice) Jayfeather stated that he made sure that they're paths never crosed.
In a way, yes. When she has a fight with Brambleclaw in which she stays mad at him and Brambleclaw is overcome with unhappiness, Squirrelflight turns to Ashfur and loves him. But when she makes up with Brambleclaw and loves him again. Ashfur is furious and heartbroken.
Squirrelflight's father was Firestar.
Squirrelflight is Leafpool's sister!
No, but he tries to kill Hollyleaf, Jayfeather, and Lionblaze because he thought that if Squirrelflight watched her kits die then she would go to Ashfur. But Hollyleaf, Jayfeather, and Lionblaze are not Squirrelflight and Brambleclaw's kits.
Assuming that you are talking about Squirrelflight's big lie, Squirrelflight lied to protect Leafpool as well as Jayfeather, Lionblaze, and Hollyleaf from the truth.
He never meant to kill Hawkfrost, he accidentally impaled his throat while trying to save Firestar. Later, he realized, Hawkfrost would have been very dangerous to the Clans. He also killed him because Hawkfrost was trying to kill Firestar (Brambleclaw's former mentor and current leader).