Do whatever you would like to improve the game. There are almost no rules, but you will be graded based on how difficult it is to do what you do. In other words, something that LithTech essentially does for you is not worth much (like multi-texturing or LOD).
Some things you might like to do:
Start with your solution to stage 3, and modify from there. There is no need to keep a copy of your stage 3 around (unless you want to do so for your own sake).
Again, work in your group directory however you see fit. Grading is by demo during the first two days of exam period.
You're essentially on your own for this one. As part of your design process, look at the LithTech docs to see whether or not it provides facilities to help you (such as a particle system implementation).
You may submit your project late, with a penalty of 5% of your score per day or part thereof that you are late. The penalty is exacted before your grade is truncated.