Kagome would probably be shocked at first. Then she would start yelling at Inuyasha, demanding to know why he's doing this. She's not the type to just sit there and take it.
He might be shocked at first. After all, he has probably only heard stories about his father. Then he could be angry, blaming his father for not being around when he was growing up.
Inuyasha would probably be very angry at first. He has always had a possessive streak when it comes to Kagome. He might see Koga as a rival and try to fight him. But as time goes on, he could start to realize that Kagome is happy with Koga and, though it would be difficult for him, he might eventually back off and respect her choice.
Tanjiro's fate in the manga is that he ultimately passed away. This event was a significant part of the story's development and had a profound impact on the other characters and the overall plot.
Tanjiro's strength in the manga is significant. He acquires new powers and techniques, and overcomes numerous powerful foes with determination and strategy.