As of Sunrise, no.
No they don't have any kits. You may think that they did have Jaykit, Hollykit, and Lionkit but those are actually Crowfeather and Leafpool's kits. Squirrelflight covered for Leafpool and took the kits.
Squirrelflight was foster mother to Jayfeather, Lionblaze, and Hollyleaf, but as revealed in Sunrise, they are actually the kits of Leafpool and Crowfeather. I suppose Squirrelflight is barren because she had been mates with Brambleclaw for so long and still doesn't have kits. But since they are not mates anymore, Squirrelflight probably won't have any kits.
Brambleclaw has no kits biologically, since it has been revealed that Squirrelflight did not bear him kits; instead, the kits were her sister Leafpool's. However, his adopted kits (the aforementioned kits) would be Jayfeather, Lionblaze, and Hollyleaf (presumed deceased).
Yes, Brambleclaw has three kits named Tigerstar, Tawnypelt, and Hawkfrost. They were born to him and his mate, Squirrelflight.
No, they did not. Squirrelflight was their "foster" mother. Lionblaze, Hollyleaf and Jayfeather's real parents are Crwfeather and Leafpool. So Brambleclaw and Squirrelflight never had any kits.
squrrielflight didn't have any kits. lionkit, hollykit, and jaykit, were her sister's kits.p.s. I am not telling you squrrielflight's sister's name
Squirrelflight did not have any kits of her own. She raised Leafpool's kits, Jayfeather, Lionblaze, and Hollyleaf, as her own to protect her sister's secret that she had broken the warrior code by having a litter of kits.
This is not likely. The book Sunrise implys that Birchfall was the father of Whitewing's kits when Birchfall said; "We've called the gray one Dovekit, and the tabby and white one is Ivykit." Although this does not explicitly prove that Birchfall is the father, it certainly implys it and the books have given us no reason to believe otherwise.
Leafpool was careful enough to hide it. Squirrelflight ate extra prey to make it look as if she was pregnant, and one night when it snowed, both sisters left camp and made it look as if they had been stuck outside in the snowstorm and couldn't get back to the camp. Leafpool had her kits during that time, and when they returned to the ThunderClan camp, it was with the story that the kits were Squirrelflight's. Since Squirrelflight had not been pregnant, she didn't have any milk, but they pretended that her milk didn't come. Leafpool took borage leaves to stop her own milk from coming. It was a cunningly devised plan to hide her deception.
Ashfur did not kill Squirrelflight in any book. He did attempt to harm her in "Sunset" (Warriors: The New Prophecy series) by attempting to push her off a cliff, but Squirrelflight survived. Ashfur's actions were driven by his jealousy and betrayal, but they did not lead to Squirrelflight's death.
Squirrelkit was Leafkit's(pool) sister and was the most adventures of her litter. Squirrelpaw was Dustpelt's apprentice and when she was only an apprentice for a moon or two she left with Brambleclaw, Tawnypelt, Crowpaw(feather), Feathertail, and Stormfur on the sundrown journey. She also became a warrior on the Great Journey. Squirrelflight was Ashfur's mate for a moon while her and Brambleclaw were fighting. Then she told Ashfur she couldn't be with him and went back to Brambleclaw. She then had kits with Brambleclaw; Hollyleaf, Jayfeather, and Lionblaze. Then there was a forest fire and Ashfur thretened to let her kits burn in the fire and finally Squirrelflight told him it wouldn't hurt her because they aren't her kits, they are Leafpool and Crowfeather's. Hollyleaf can't stand it anymore and she tells everyone at the gathering.
Yes, Sandstorm is Firestar's mate and their kits are Leafpool and Squirrelflight.