Congrats on progressing to the final round!
Let me take your questions on by one.
1. What to prep for/anticipate in the final round (a case and fit interview)?
There are two things to watch out for in particular for the final round (aside from improving on the feedback from the previous round which I'm discussing in the second question below):
a. Cases are more unusual and unstructured. Some final round interviewers might come up with the case on the spot or choose to skip the case altogether. Others might just give you a short market sizing question (that's how my final interview went like) and spend the rest of the time discussing with you to get an understanding of how you think and what you care about.
b. Partners appreciate brevity and care more about you as a person than your casing skills. Since you got to the final round, Partners already know you have the basic skills necessary to do the job, so they rather focus on understanding who you are as a person, how well you communicate and how well you would handle a client. Make sure that you try and connect with them and that you are concise and eloquent in your communication.
2. Is it OK to ask the recruiter for feedback from my first case and fit interview?
Not only is it ok, it's recommended. It's actually very important to get feedback on your first round performance so you know what to actually focus on improving. The interviewers will also be paying attention to see that you are coachable and can improve on the feedback that was provided.
Best of luck and feel free to reach out if you have additional questions!