Danse is a bit of an enigma. I don't think that you see enough of her as a character to be able to form a definite and unwavering character analysis, however her actions and behaviour do give rise to several different suppositions. Firstly, of course, is her loyalty to Haven House. In The Music Awards she refers to everything in it as 'our' and is personally involved in not only organising the concert but in enlisting the help of Jem and the Holograms. Her disappointment in them turning her down is also very personal. This leads me to suspect that Haven House is something bigger in Danse's life than just a worthy cause. The indication from the series (Homeland Heartland) is that Danse has no parents growing up. Her father she believes is dead, her mother 'went missing'. Therefore it's logical to suggest that maybe she was an unhappy foster child who never accepted her mother's disappearance and who perhaps was a runaway herself at some point. Haven House was the thing that got her life back together and now she wants to repay the favour.
The show also indicates that Danse still lives at Haven House, since she always seems to be there and to be associated closely with the children there, more than a simple volunteer worker might. This devotion suggests strongly to me that her loyalty to Haven House is based entirely on her own childhood experiences.
As a character herself Danse appears to be everything Jem should be, if she only had the same integrity. There is nothing deceitful or unkind in Danse's manner. Dancing is the most important activity in her life - highlighted by her distress and bad temper over her injury in Danse Time - but her friendships are equally important to her. She is sweet natured and is very fond of the Holograms - her diligence in fighting back to health in Danse Time is testament to that. Danse comes across as a girl with a big heart and the kind of person that easily attracts people to her. She is not judgemental and is deeply sensitive, especially regarding her family (as seen in Homeland Heartland when she is upset at the apparent indifference of her relatives). She does not like conflict and always tries to do her best whatever the circumstances (even continuing to dance after having a large pumpkin fall on her in Trick or Techrat).
Danse's origins are somewhat unusual, since her mother Nadia was a dancer with the Zagreb Ballet and her father a Yugoslav (now Croatian) doctor. Danse appears to have been born in America and there is no indication of her either speaking Yugoslavian/Croatian - she does not even speak with an accent - though it would be more than logical if she was bilingual. Her surname is Czech, suggesting that her family has a more mixed Eastern European origin. Even her name's spelling, 'D-A-N-S-E' is unusual, since this is the french word for 'Dance' but as far as I can tell Danse has no links with any French heritage. Having said that, though, her first name is Giselle, and I suppose it's not beyond the bounds of possibility that somewhere in her cosmopolitan heritage is a dash of french also :D
Danse's roles are varying, and what exactly her role with the Holograms themselves is is never made clear. She is generally a stage dancer, though on occasion (One Jem Too Many) you get the idea she is choreographing the movement of the group onstage. She is friendly with the group without having more affection for one member than the others. She seems to have a fair amount of admiration for Jem (silly girl!) for in the Music Awards she is thrilled at the idea of them playing her benefit.
Danse has three male associates on the show, quite a lot considering she gets less airplay than the Misfits! The first of these is Cisco, a blind guy she meets when in Hospital in Danse Time. In my opinion this is her most genuine attachment, since the other two - Robin Goodfellow and Stefan in Homeland Heartland - appear to be more contrived or fantastical than geniune. Her affection and admiration for Cisco's courage suggests to me that of the three she likes him best.
Danse is also good with children, and, aside from the Haven House gang, she also is teaching the Starlight Girls to dance at the start of KJEM. There is no suggestion of any real opinion on her part of the Misfits, and she never meets the Stingers.