A1) Yes, she has romantic feelings for him. He also feels something for her, but it's unclear what it is exactly or how deep it runs.
A2) Takahashi does insinuate a small relationship between the two as Kagura often relies on Sesshomaru and comes to him for help. And at her death, she says she was happy she could see him again and Sesshomaru returns her feelings by saying he purposefully came to see her.
A3) We could infer that she have feelings toward him referring to The Final Act Episode 2. Sesshoumaru rushed to her side, attempting to rescue her. However, he could not since shouki (miasma) had gone through the entire body. She past away with a pleasant smile.