I have some question about ICL

Hello, I am a Korean student who got an offer from ICL Maths (Msci 4YFT).
I had no specifications(I just passed GED), but I got a not-bad MAT score. (Maybe this is the reason I got an offer.)
I was hoping to receive a country's scholarship for attending a prestigious university, but I was rejected and now I have to bear the total cost of tuition. I am being cautious in making a decision due to the expensive tuition. I have some questions regarding this.
1. I want to try and learn various things. Ex) studying quantum information, business management,... I also want to engage in various activities. Is ICL flexible enough to accommodate these activities?

2. I want to do research on knot theory and physics. Is ICL provide an active tutoring program?

If I will not enter the universe, I will enlist in the military next year as a Korean, and I might consider reapplying for admission (maybe Cambridge, I haven't applied yet) during my military service.

Thank you for reading this question, and thank you very much in advance!