A1: In the end Kikyō dies and Inuyasha gives her a farewell kiss. That was the last time Inuyasha saw Kikyō. Inuyasha didn't necessarily even choose between the two, because Kikyō died before the end. Since he had two lovers, he resided with the other one, Kagome.
A2: Inuyasha chose Kagome. After Kikyō died, Naraku was defeated and the battle was over, Kagome returned to the Feudal Era and started living with Inuyasha. Kagome was the first human whom he met who accepted and loved him for who he was (born as a half demon) and also the first human who shed tears for his sake (just like his human mother did).
A3: Additionally, after Kikyō was resurrected by the demon Urasue, Inuyasha was shocked to see her alive, and was shown to still have lingering feelings for her. That being said, while Kikyō was alive, Kagome and Inuyasha did stay together for the entirety of that period.