Your approach on splitting it into three parts already sounds really good! I think you should always start by talking about your interest in the firm's work just because at the end of the day, they want to know that you're actually going to enjoy doing the job more than anything else. But as long as you're providing enough detail on the work aspect, I don't think there's anything wrong at all about going into detail about the culture at the firm. In fact I think once you're at a telephone interview/AC stage, it's actually a great opportunity to really go into detail about the various events you've met the firm at, the people you've spoken to and what exactly resonated with you about their culture. Remember that talking about a firm's culture could also include mentioning their emphasis on diversity, pro bono or anything else that doesn't touch on purely billable work and mentioning these things always go down well with firms.
NRF in particular never seemed to have a problem with me talking about their culture both in my app and interviews, so if it is something you want to touch on go for it!
I know it's easier said than done but try to relax as much as possible before the interview and don't panic! It sounds like you've got your answers planned out pretty well and I'm sure it's gonna go a lot better than you think! Good luck and let us know how it goes!