A1: Well, in the end Kikyo dies and Inuyasha gives a farewell kiss (so gross). That was the last time Inuyasha saw Kikyo again. It actually means that Inuyasha chose Kagome over Kikyo. PLUS Kagome is cuter than Kikyo.
A2: Inuyasha chose Kagome. After Kikyo 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: Inuyasha didn't really have a choice because Kikyo died before the end. Since he had two lovers, he resided with the other one, Kagome.