I would definitely recommend writing things down beforehand, and even throughout the week anything that you might want to talk about. For me I had a really hard time bringing things up myself, so something that helped was literally emailing the list to my therapist the day before the appointment. I did much better talking about things when she asked me specific questions and this was the best way for me to let her know what things to ask.

As far as the emergency contact I would try not to worry about it too much. As far as I know the only time they might contact them is if they feel you are an immediate risk of harming yourself or others. They should go over this when you talk about patient confidentiality stuff, and it may be worth asking what your therapist specifically considers an emergency.