I go to college and lived with a gentile roommate last semester, and I wish I had someone as considerate; but, let's get started. Obviously make sure to be considerate on Shabbat by leaving the bathroom light on and avoiding any sort of problem that must be solved by breaking one of the Shabbat rules. For example, don't leave something of importance that she might need on Shabbat outside the house if there is no eruv, because for her to bring something from outside back in would violate the prohibition of transferring in between domains. Another foreseeable scenario is if you lock the front door on Shabbat when she might leave it unlocked during Shabbat so that she doesn't need to carry a key. I'm not very creative with these sorts of scenarios, so make sure to ask your Jewish friend if you ever have a concern.
I'm assuming your friend is also shomer negiah and follows the rules of yichud so avoid bringing in male friends or at least ask for the house to yourself if you really need a male buddy to come on over; and, make sure your male friend (if the situation ever comes about) knows not to hug/touch your Jewish friend. I'm not saying you have to obey yichud or be shomer negiah, but having male guests can create a problem for your female friend. It's very awkward watching my roommate cop a feel from his girlfriend when I'm davening only a few feet from him. This isn't as much of a problem if your friend has a husband or male relative living in the house as well, but better safe than sorry.
As for pesach, avoid bringing in any leavened breads into the home, and if your friend abstains from kitniyot, then avoid bringing in those foods as well. Chametz must be removed from the home before Pesach and cannot be introduced into the room until after the holiday is over. As for kitniyot, there is no prohibition, as far as I understand it, of having it within the home; but, I don't know what your Jewish friend's preferences. It's better to ask or just play it safe.
Cooking is also a very complicated question. I'm not sure if she double-wraps or if her home has separate ovens for meat and dairy, so ask her about cooking. Maybe she wants you to use your own kitchenware, maybe she wants you to use a specific sink to wash your kitchenware, maybe she wants you to use her kitchenware and be aware of which is for meat and which is for dairy. Either way, this is a very complicated question and all I can recommend is that you ask her about that. As for your question about your kitchenware un-koshering other kitchenware, I'll explain the problem (or lack thereof) and the solution. In halacha for kosher, at least for meat and dairy, taste is principle (Yoma 73b; Yoma 80a). You transfer the taste by washing and cooking the kitchenware to cook meat and dairy, but this can be more technically explained here. You can (according to law, not according to the rules of the household) use kosher kitchenware that the family uses as long as you do not prepare anything fit for a king's table (or anything else not kosher, of course). The reasoning for this is that if you prepare food that is bishul akum, then the utensils are now not kosher. That's why there's an advantage to you having your own kitchenware, but then there's a load of questions with whether or not you're using her oven, if you're cleaning in her sink, et cetera. I don't feel comfortable enough in this area to discuss it in detail, so ask her or a rabbi for more information on this subject.
Avoid playing music in the house during the Counting of the Omer and during certain holidays and periods of times (like the Three Weeks and the 9 Days). She might not even consider it a prohibition to listen to recorded music, but it's better to ask than assume. If you really need to listen to music, get a pair of headphones.
Besides that, you should be okay. Maybe there are some female oriented concerns for Jewish life that I'm not looking at, but I'm not very well versed in any of that. Be considerate, be nice, have a good relationship with your friend and reach an understanding between the two of you. I wish you the best of luck.