Yes, in Inuyasha The Final Act episode 10. But he kissed her when Kikyo was already dying.
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on episode 33
No, he chooses Kagome. Kikyo's not really alive--she lives off the souls of other people's --and Kagome makes more sense, anyway. Also, Kagome and Kikyo are very different people, regardless of Kagome being Kikyo's reincarnation .But...yes, Inuyasha chooses Kagome, he loves her for who she is anyway--not for Kikyo. Well...in Ep 47-48 he chooses to be with Kikyo, but that doesn't happen, because Kikyo will die and Kagome is ended up to be with Inuyasha, and Inuyasha and Kagome were born for eachother not Inuyasha and Kikyo. Although Inuyasha does love Kikyo, but also Kagome.
InuYasha never actually picks. It's a complicated situation. In the end Kikyo dies for good, and does not come back to life. So, he's left with Kagome. In the end, InuYasha and Kagome get married, but who knows what would've happened if Kikyo lived? I think he would've chosen Kagome because their bond was greater than his bond with Kikyo. In the end, he never picks. He is merely left with no choice but to stay with Kagome. Although, he will never forget Kikyo.
No. Kagome and InuYasha did, sort of.
Not really, though she may have been jealous of her at one point, due to Inuyasha loving Kagome as well as her.