Let me give some thoughts for the rest of the ones from chapter 4:

4.9: This one is tricky, so maybe focus on others first. Consider $9, f_1(9), f_2(9), f_3(9), \ldots$. Explain why this sequence eventually starts repeating? What are the possibilities for how often it repeats? How do all of these possibilities relate to $2520$?

4.10: As a hint: an intersecting point comes from two lines, so four points. Are these four points unique for that intersection point?

4.11: Focus on what matters here and don't get scared by other parts. Do we know a trick to find solutions to $x+y+z=n$ for integers?

4.14: Hint: we want the girls to be separated, so arrange the boys first and put the girls into spaces.