Hi,
I recommend to do some internet search for application notes and tutorial videos.
1) Without capacitor it makes no sense. With capacitor the current is no e-function anymore.
How does the current in the coil change when a reverse voltage or a large capacitance is connected to the output?
in ideal case: I_L = integral (dV/dt) / L
Difference with / without capacitor:
* without C: dV/dt depends on current --> e function
* with capacitor: V is about constant --> almost linear
2) again: there are a lot of really good videos around that explain every current in detail and waveform.
3) consider input voltage variation, output current variation, expected output voltage variation.
4) what could be the problem of very high frequency?
Hint: Many years ago buck converters worked with a couple of 10kHz then more than 100kHz, now many work above 1MHz
Klaus