Hi there!
I'm a Natsci at cambridge who arrived with the intention of studying chemistry or materials science and has ended up in earth sciences. The career progressions are as broad as the course (which makes career sessions difficult) I know people go into everything from banking to post grad medicine to research to journalism. I certainly wouldn't consider it a restrictive degree in terms of it ruling out a lot of career options.
Cambridge mostly cares about you showing super-curricular interest in general, but related to what you're intending on studying. So that can be anything between reading around your subject (especially if you can discuss it and critique parts) and also some work experience, maybe science technical stuff, maybe outreach stuff around science or tutoring. It's again, as varied as the course, and depends on your interests.
For NSAA, it changes pretty frequently and I think it's already on a different iteration to the one I took precisely to avoid schools banking information to give their students advantage. In general, practice doing problem solving questions, it tends to involve GCSE level stuff but with more difficult thinking processes. Things like the chemistry and maths olympiad provided me with good practice material as well as the official stuff.
I've loved this course so much. I really didn't know what I wanted to do in science, I never expected Earth to be the one, but it was. I also got to learn the next level of maths and chemistry without having to give it up at that level, which is so helpful to a wider knowledge base on which to build my specialist knowledge.
The other students are amazing and just the discussions at dinner are great. It's wonderful to be around other people who love their subject and are prepared to talk about it at depth in a casual context.
People sometimes worry about competitiveness, but that has never been a thing in my college in natsci. This is partly due to very positive director of studies' attitude to working together. Also, the move from having to be the best all the time at school to 'there's this bloke in that college that will always be the best so you can forget about that and just focus on what you enjoy and need to work on' was very relaxing and fulfilling for me.
Hope that helped, let me know if you have any other questions.