1. Rina stopped dating around. We have seen in the manga where she has talked to Yuki about how she had a stable boyfriend but broke up.
2. Yes but she told Yuki she is sorry. She may not relate while saying her feelings are valuable. Rina told Yuki that its okay to not talk to her mother.
3. The whole "introvert" does not mean you like to be around yourself. You can be a social introvert. Introvert vs extrovert means how you handle your energy with people. We have seen characters like Tsubasa who are extrovert but not be bubbly. He's not even accepted by others. He gets his energy by being around people.
I understand wanting to be around the other girls because she wants someone to who can relate. However, Rina has been telling Yuki that she is her friend and accepts her. We have seen a chapter where she assumed that it was a one-sided friendship.
I didn't list those things with the intention of discrediting Rina of course, I just think it's healthy for someone to have a wider circle of acquaintances for specific needs (Ayana for cosmetic surgery advice, Runa for venting about financial stability, Taiyou for movies and mother stuff).
Yuki grew up isolated most of her life and has just started living on her own so her knowledge of the world is still very limited. She understandably is gonna crave concrete examples to mirror herself in, not just "I don't know what you're going through but you can do whatever you want". She doesn't know what she wants because she has barely went outside her shell yet! Instead of putting all her expectations onto Rina to explain how she should live her life, Yuki having conversations and experiences with many people is a good thing.
And of course, all that being said, a "person you can relate to" won't necessarily mean they will be the best match in other aspects as we're currently seeing with Taiyou. I believe Rina will come back as the strongest evidence of friendship Yuki nurtured at some point.