We are our own worst critics, so the interview may not have been as bad as you think! With rehearsing answers, you don’t want to do it to an extent that you sound scripted in the actual interview. Of course, your answers for why law and why the firm should be solid, but you genuinely cannot anticipate every question you’re going to be asked especially where it’s conversational and certain questions follow from a previous one.
Regarding nerves, I used to put a sticky note by my webcam reminding me to smile and that I’m capable. I thought it was corny so it actually kept me smiling in the interview. You may not get everything right but don’t let it affect your confidence for the rest of the interview. Also, humanising the process definitely helped me because the partners interviewing you (although experienced in their practice) are normal people. Nerves will definitely be expected but taking deep breaths before joining the call (or going into the interview room) and remembering how far you’ve come should help.
I’m not sure what you mean by partner-style of questioning but from my experience, it tends to be more conversational and flow from points you’ve made or something you mentioned in the application. My advice for this is prior to an interview, reflect on all your experiences (work-related, volunteering, extra-curricular, etc) and think about what you did, why you did it, what you enjoyed/didn’t enjoy, transferable skills, etc. If you can speak about any of your experiences substantively, you’re in a much better position to respond to a question even if it’s one you may not have prepared beforehand. I hope this helps!