If you want 50% charge in 10 minutes, you are charging at 3C which is pretty ambitious (30A charge current for that battery). The internal resistance of most RC flight batteries is low enough to do this, but you are going to have to carefully monitor the temperature of the battery pack; probably with multiple temperature sensors.
You will also have to monitor the internal resistance of the battery pack during the charge cycle (measure the pack voltage and charge current, use ohm's law to get the internal resistance). If you see the internal resistance go down significantly during the charge cycle or you see the temperature go up, stop the charge cycle immediately.
Building a 30A switching converter that operates stably in CC/CV regulation is also a significant technical challenge. If you don't have significant experience with switching power supply design the odds of success are not great for a student project like this.
In any case, this is something you will not want to operate indoors (ever) and charging the battery in an environment where you just expect a battery fire is highly recommended.
Charging at 3C will also require active monitoring of the voltage of each cell individually and balancing during or after the charge cycle. Minor differences in cell capacity/impedance will be exacerbated by the aggressive charge rate.
You will also have to wait for the battery to cool between the discharge (flight) cycle and the charge cycle. You will probably also have to wait for the battery to cool between charge and flight (and this will pretty much render the 10 minute charge cycle as useless). The Tesla batteries (AFAIK) use water cooling to deal with this.