No, Kagome didn't like Inuyasha at the start of the series because she thought that Inuyasha is a pervert and didn't like him. But she got surprised after Inuyasha hugged her in episode 19 and started liking him.
A2) No, Kagome didn't like InuYasha, because of his rude & selfish attitude and personality (at first). But, later after few episodes (from season 1), she's started to care & like InuYasha, even worries about him when he's in danger & even started developing love feelings for him too. In episode 48: Return to the Place Where We First Met - she realized that she's in love with InuYasha. So, now Kagome likes/loves InuYasha.