As of now, Uta is indeed alive. The story hasn't depicted anything otherwise. Maybe there'll be changes in the future, but for now, Uta's part in the manga continues with them being alive.
Their relationship could start with Uta being initially distrustful of Luffy. After all, Luffy is a pirate and Uta has her own ideas about pirates. But as she sees Luffy's pure heart and his determination to protect his friends and pursue his dreams, she starts to warm up to him. They might then become friends who share their different stories and experiences.
" Uta's Dream " and " One Piece Uta, The World's Songstress " were two novels recommended for playing Uta. Both novels had stories and character settings about Uta.
Eventually, Naruto could grow resentful. If the ignoring persists for a long time, he might start to think that Kakashi doesn't care about him at all. This could change Naruto's attitude towards Kakashi and might even make him more rebellious in his training or actions. However, deep down, he still probably hopes for Kakashi's recognition and approval.