In Kapitel 94, Eve didn't carry her sword. I'm thinking about a theory that Teito is Eve's sword or her sword's reincarnation. Like Verloren's scythe, as a God or Goddess's weapon, he could talk and that also means he can have a soul. After the death of Eve, the sword made a wish to the Chief of Heaven that he will keep her soul with his to protect it while staying in this world. The light from his soul which was sealed away along with Pandora's Box is Eve's soul. If he can escape Verloren's core, Eve's soul will be release to purify Verloren's darkness. During the two Kapitel 94 and 95, Eve has guided Teito to help Landkarte and Frau. It also explains why he feels so closed to her like they've met before. Moreover, while still being the sword, he admired her so he wanted to be like her (he might also ask the Chief to give him an appearance that almost looks like her), like Frau wanted to be like Gido. So his personality is somehow like Eve's because he has been by her side for a long time and learning a lot from her. He wants to protect precious things to him by his own hands like his master. And Eve seems to have no special feelings for Frau in Kapitel 95 because she's just inside Teito, not himself.
Besides, Verloren's scythe has said to Teito, 'I have been looking for you for a long time'. It maybe because he knew Eve's soul was inside Teito back then. Or Verloren's Scythe also has something with Eve's Sword so he wants to find him.