Inductor and Capacitor for Bidirectional DC-DC Converter with Battery
I do not expect the ripple current in the inductor to affect the peak battery current. You will need to put a lot of caps near the input of your converter, so that they can provide the AC peaks while the battery will only see the DC. This also helps a bit for load transients.

The switching frequency entirely depends on the coil size, saturation current, output current, duty limits, vin, vout. But you have it the other way around: usually the switching frequency is given, as vin, vout, current requirements and duty limits, and then you select the coil.