I don't know in which step you have trouble with Gabriel's Quest so I'll list here step by step:
- Go to Gabriel's House every Tuesday to learn about photography to the point he'll give you a challenge to complete.
- Talk to Kate in the Mall and make a deal with her to take her photo
- Go to Kate's Home on Thursday and ask where she get her dress. Take the photo and said that she looks cute.
- Go to Bar, Beach and Park on each Thursday to meet Kate and bond with her.
- Go to Kate's House again and take the photo
- Go to Gabriel's House immediately and show him the photo
- Go to Gabriel's House again on Tuesday and you'll get a threesome scene with him and Haniya
As for Kate, she doesn't have specific quest for herself but she's involved in some of the quests, like Gabriel's, Alice's and Zen's Quest, as well as one of the girls you can have relationship with.
For Chloe, you just have to go to her house on Wednesday until Anna decides to join the fun and shows her who's boss.