A1)NO! Kagome NEVER loved Hojo. Even, the first time, in the beginning of ep. 13; Hojo asked Kagome to go out on a date with him on Saturday; Kagome asked InuYasha if he can let her come back to her world on Saturday and he agrees. But, its unknown or unseen that if Kagome did or didn't go on that date with Hojo on Saturday. (Which I bet she didn't). But, in the middle of ep. 20, Hojo again asked Kagome to go out on a date, but she's unsure about; then Kagome's very nosy friends: Eri, Yuka & Ayumi (from her modern world) are thinking that Kagome has love feelings for her "jealous boyfriend", but Kagome doesn't want to admit that she does has feelings for InuYasha (but she does has feelings for InuYasha, she doesn't want to show or too shy to admit, it epspecially at public), plus from the previous episode: ep. 19, Kagome is still upset about InuYasha was only hugging her, just to get her half shikon jewel necklace from her & force her to go back to her world and never come back (even, it did happened, but he REALLY hugged her for real, because he was worried for her safety, causes she was badly hurt by his half-older full demon brother: Sesshomaru, he even says that ("he was afraid that he was going to lose her") which that was the reason why InuYasha took the half shikon jewel from her & force to go back to her world and never come back). So, Kagome decided to go out on a date with Hojo. But then, in episode 21, when Kagome goes out on her date with Hojo, she was thinking & worrying about InuYasha, because he was badly hurt by Sesshomaru, but she tries not to think about it, but she couldn't stop thinking & worrying about him. So, Kagome is so worried about InuYasha, so she lefted her date with Hojo, ( a little bit short in the middle of the date) to desperately go see InuYasha and to check if his wounds are healed or not. So, as the rest of the series goes on & even in the Movie 2 of InuYasha, as anytime when Hojo shows up & asked Kagome to go out on a date with him, she doesn't go out with him. Plus, she only LOVES InuYasha. So, that's the reason why? Hope this helps?