A1) Yes,Inuyasha loves Kagome.Another way Inuyasha loves Kagome is that Inuyasha is always protecting her when she's about to get hit. He also shows his love by caring for her when she's sick.I hope that answers your question.
A2) Yes, of course InuYasha loves Kagome. In fact, he's far more in love with Kagome than Kikyo. Which means he has more stronger, deeper & pure love feelings for Kagome than for Kikyo. Reasons why?:
- he's firecely protective of her.
- gets so very jealous when any boys who falls in love with her, especially Koga.
- always go to the modern era (Kagome's world) to pick her up and even, spend some time with her & her family over there.
- he was devastated when he thought Kagome died from Mukotsu's poisonous gas in ep 107.
- fearing of losing her or unable to protect her from danger.
- gets very upset when Kagome gets captured, held as hostage or about to be killed by any enemies, especially Naraku.
- she healed the wounds of his heart & soul by showing him true kindness & compassion.
- she taught him how to smile, to trust people, to make friends, rely on friends, shed tears for others and taught him true kindness & strength.
- InuYasha loves Kagome for who she is, not because she's Kikyo's reincarnation. Even, in ep. 48; Kagome explains to InuYasha that its true that she's Kikyo's reincarnation, but she's still not Kikyo, because Kagome's heart belongs to herself (which InuYasha knows its true). Plus, Kagome & Kikyo are completely different , even they have 1 thing in common: both in love with InuYasha. But Kagome's love for InuYasha is far more stronger, deeper and pure than Kikyo's love for InuYasha.
- he takes care of Kagome when she's sick. During the series, while after meeting Kagome, she became his new, but true love interest. True, Kikyo was his first lover in the beginning before meeting Kagome, but after been betrayed by Kikyo (which its was a trick by Naraku), Kikyo is no longer his lover anymore. Kagome became his new and true lover during the series (of course, Kikyo accepts that Kagome is InuYasha's real true lover). And finally last: in Ep 26 of the Final Act, while battling the demons in the inside of the shikon jewel to rescue Kagome, he realized that he was born to meet, to love, to protect and to be with Kagome FOREVER, same as for Kagome too. Theses are the reasons why InuYasha loves Kagome
Note: You don't want to get upset over Inuyasha kissing Kikyo a couple of times, especially when she dies. Those are only to tell each other to forgive each other and reconcile for their pasts.
A3) YES of course! InuYasha LOVES Kagome! In fact, he has much more stronger love feelings for Kagome than for Kikyo. At the end of the Final Act, he married Kagome, after they're reunited after 3 years.