A lot of the particulars depend on the culture of your school or rotation. Speaking over someone else is always rude; as is answering a question directed to another student. On the other hand, if the attending is asking questions to "the group", whoever knows the answer pipes up, and there's nothing wrong with that. This means the person who is fastest with the answer gets more of the questions, and tends to reward memorization of Surgical Recall or Family Med Recall, as the case may be. That said, it can be really frustrating if you're the sort of person who needs a couple of minutes to think to come up with the answer. I'm not sure there's an easy solution to that one. The best way I've seen it go down was we two med students were friends, and just decided regardless of who knew the answer, we would both count to ten before answering... tended to be more equitable, but you have to be friends to make it work.
As far as responding to every task that might need to be done, that's your job as a third year med student at many schools on at least some rotations. At my school, at least on surgery, if you're standing there while the chief resident is opening a 4x4, you're not doing your job (and you'll be told that). If the chief sounds like she might need a flow sheet, you run around and find the flow sheet. While the intern is putting up the dressing in the last room, you run down the hall ahead of the team to the next room and get the dressing down. And so on. On family med, however, things are more low key, and that's not the case.
So, to sum things up, try to be friends with the other med student on the rotation. What she's doing could either come from having been taught to do that, or from nerves. If you feel like she's really stepping on your toes, and you can thing of a better way to coordinate it, try talking to her to coordinate something. On the other hand, if she's just trying to make your attending's life easier, join in. As far as buying cookies and such, if you're going to do it, coordinate with the other student so you both brought them in. If you're giving a presentation on a topic, give the other student a heads up so she can do one also (and can read up on the topic to answer relevant pimp questions). Mostly, though, just keep your head down, work hard, and take care of your patients and your team... don't get pulled into the drama.
Best,
Anka