1. She didn't realize how much the kind Eiji's unconditional love for her meant to her until she was finally confronted with the possibility that the kind Eiji Urashima was going to be gone forever. She thought if she fused the personalities, she would get the best of both worlds with the driven B1 that LL loved + the kindness in Eiji's heart. The funny thing is, in the ending that was not uploaded here but in other manga sites, it is suggested that she might have succeeded and that the alter Eiji was finally slowly integrating back into the real Eiji's persona.
2. If you can recall, B1 and Kyouka have never actually met until the showdown at Kyouka's childhood home. They even said so just when she 'killed Eiji' and met B1. It was a bluff.
3. The initial reason would probably be just simple curiosity and altruism towards the kind Eiji (and maybe liking him a bit). The primary reason till the end would probably be her childhood guilt over seeing the fake Rin Shirabishi (who was friendly to her when she was a kid) all tied up and tortured and being unable to do anything about it. And she also has a lot of free time apparently.
