Carmen is more of a family person, and a follower, so yes at first she wil be quite introverted, but I think that BECAUSE she is a follower and because there are many outgoing personalities in this roleplay, that she will quickly adapt to the surrounding atmosphere. She will quickly realize that the people at camp are family. Once she realizes that, she will interact with them like she does with her mortal family. 

As for her weapon, her mortal famiy doesn't know much about camp half blood. Only that it exist and is the best place for Carmen to live. Her current weapon is only for getting her to camp. Once there she'll probably have to talk to Ky'vie about making a weapon similar out of Celestial Bronze.

I hope that clears everything up.