I don't have the books on hand to write out the essay i'd like to, but Tigerclaw is one of the most misunderstood characters in the fandom.
I don't mean in a "poor little meow meow" way, I mean they legitimately don't seem to understand why he does what he does
More than anything, Tigerclaw is an opportunist. He will take advantage of any situation in order to get power.
Outward, vocal hatred of kittypets? That's more of a Darkstripe, Longtail, Sandpaw/Dustpaw thing. Tigerstar hated him, but in a much more quiet way. At least in Into the Wild, he's much more in line with what Bluestar says. Also, Sasha wasn't a kittypet but a loner when he was with her. Also also, she wasn't going to reveal his political assassination plot or get in his way, if that makes sense.
"why would Tigerclaw combine RiverClan and ShadowClan if he hated halfclan cats?"
Because it wasn't about halfclan cats in general, it was about these specific cats that had a connection to his enemies (ThunderClan and Bluestar, specifically). In fact, most of his interactions with other clan cats are relatively chill? At least , compared to Thistleclaw and Brokenstar. Especially when he thinks he can use it to his advantage (see ShadowClan and ex-shadowclan rogues in Tigerstar's fury)
"why didn't StarClan take his nine lives/Why did StarClan refuse to give him lives"
It appears that lives can only be revoked at a specific holy site (ie. The moonpool or moonstone). As for why they gave him his lives, A. At this point in the series, cats still had free will. Tigerstar was warned multiple times, including by StarClan cats, that he needs to make a very big change very soon or he'll face the consequences. B. StarClan knew what would happen, and saw him dying nine times to Scourge as a more fitting punishment than denying him his lives
"pinestar was told to kill tigerkit"
That's straight up not what happened. Pinestar was told to raise him well. Other voices- possibly his own self doubts- suggested killing him, but that wasn't commanded to him and it's also not why he left ThunderClan
"Tigerstar killed Gorsepaw because he looked like Fireheart"
Neat headcannon, but that's not what happened. Gorsepaw is canonically brown, and Tigerstar killed him to intimidate/punish WindClan
"tigerstar assaulted Sasha"
No. Just. No. Everything in their relationship was consensual (but not necessary healthy). People made this up so that they could pretend she's a lesbian. That's it
