1.) That's the same Hajime Saito. How could you think it isn't?? He's the 3rd Squad Captain of the shinsengumi. It even says, Saito Hajime in the credits. Your friend needs to watch it again or something.

2.) As tic tac said, Kenshin and Saito's fight in the alley was interrupted. In fact, the two fought numerous times (Kenshin says this in the anime) but neither of them ever came out on top. The fight at the end of the OVA was a recreation of the flashback fight in the series (at the beginning of the Kyoto Arc)

3.) That was Shishio. In the manga, he actually speaks, saying something along the lines of: "it doesn't matter which side I'm on, because in the end it will be my government that comes out on top"

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