A: At the time of her death, Kikyo's heart was filled with hatred towards Inuyasha, whom she thought had betrayed her. After being resurrected, and that too against her will, using Kagome's soul, Kikyo tries to kill Inuyasha again. But, the feelings she had for him long ago, lingers in her heart and she feels jealous when Kagome's closer to Inuyasha. This fades away as the series progresses (or Kikyo realizes what's going around her) but Kagome feels Kikyo holds a grudge against for being an "imposter" or something like that. So, I would say no.
A2: Well; after Kikyo was resurrected from the dead, she felt bitterness of her death and feeling hatred towards Inuyasha, because she believes that he really betrayed her and killed her back 50 years ago. But, after learning that Naraku, an evil half demon who tricked them to hate and betrayed each other, her hatred for Inuyasha is gone and now on Naraku. And learning that, her reincarnation: Kagome Higurashi is now falling in love with Inuyasha, as Inuyasha is now falling more in love with Kagome. And they're spenting time together and becoming very closer with each other. At first, Kikyo was jealous and not very fond of Kagome, even she tried to kill her, but later learns to accept of Kagome taking her place in the living place (but Kagome won't never tried to replace Kikyo on purpose, she understands how Inuyasha and Kikyo feel for each other) and becoming Inuyasha's new lover. So, even feeling bit of jealous towards Kagome, Kikyo show to care about Kagome. Besides, when Kagome and Kikyo are in danger together, they team up and help each other. So, I say "NO", Kikyo doesn't hate Kagome.