M.P.
I have a 9 yo granddaughter. I also volunteer on the playground. My granddaughter is popular but yet she comes home at times crying because someone said something to her which hurt her feelings. These are young kids who haven't yet learned how to be polite. They are also approaching menses and their hormones are at work. I've seen an increase in tears over the last few months.
I was a shy girl who didn't fit in and spent my early years on into adulthood depressed off and on. In my 30's I learned that the way that I looked at things seriously affected the way I felt about what happened. I expected to not fit in and didn't make overtures to encourage friendships. I was still that way in college.
My mother was depressed and lacked self-confidence. When I cried she encouraged me to change what I was doing in ways that sound similar to what you're doing. I grew up feeling that I needed to change.
In reality that isn't true for most kids. Their are many girls like your daughter at school and some in her classroom. I suggest that instead of coaching her that you praise her. Help her to feel good about herself just the way she is. There is no "right" way to behave for these kids. Kids either have things in common and feel a connection or they don't. Your daughter can make friends if she's confident in herself.
By the way, my popular granddaughter also picks her nose. She can be very overbearing at times too. I've found that all the girls are on the outs with one or another one most of the time. This is just the nature of this age. I don't know of any girls this age who are focused on popular music or the latest fashions. My granddaughter has decided that she's a tom boy and declared that she won't wear "girly" clothes. She also wears mismatched shirts and pants. I was wanting to teach her some things about coordinating clothes until I was at the school. Hardly any girl wears anything that would be considered fashionable by adults. There are a few that I think must allow their mothers to dress them. I think it's better for kids to make their own choices.
Kids this age are beginning to try out new ways of doing things. They are socially unskilled. and many lack self-confidence. I suggest that the best thing that you can do for your daughter is to be sympathetic but to not make an attempt to change her. I would also stop thinking of her as not fitting in or of being different from the other girls. She is a wonderful girl just the way she is. She doesn't have to change herself to have friends. She does have to feel a certain amount of confidence and you can help her with that by focusing on praising her.
You might also be able to help by arranging play dates. Since your daughter is shy, she may not know of anyone that she wants to invite. If you can, spend some time, observing, at school. Being on the playground reveals a lot.
I also recommend that you talk with her teacher to get another person's observation and view point. The teacher sees many girls everyday and can give you an idea of what is going on from that view point.