Current output of a solar panel when connected to battery and load
First of all you need to be very careful when designing with Lithium-ion batteries.  If you exceed their specified charge or discharge rates they can leak or explode, and nobody wants that!
You definitely need a charge controller.  This will regulate the battery charging to safe levels, and follow a recommended charge profile, which is typically to charge first at a constant current until the cells reach a certain voltage, and then to top off at a constant voltage.  This is called "CCCV" charging.
You also need something to limit the discharge rate of the batteries.  This can be a very simple circuit, but for safety you need something.
Your buck converter can supply both the load and the charger.  Any excess capacity of the solar panels will just not be used.  The panel output voltage will probably rise above 48V at lower loads.
For 7 cells, a linear charge controller is not good as at low battery voltages the power dissipated will cause overheating.  You probably need a switcher there too, either buck or SEPIC.
If you can design a pcb for this, so much the better.  I appreciate that your school would probably not really appreciate it if you went and bought this on Amazon!