Hello,
1. I think, there is no exact relation. In single shot mode, it's obvious that you must have >2 points per cycle of waveform. If you equate bandwith with maximum frequency of sine wave, that could be displayed, this would be correct. But it also depends on how instrument software reconstructs waveforms from samples.
In repeated mode, when using equivalent-time sampling, there is no relation at all.
2. I assume, you're not measuring frequency but waveform. For signal frequencies near bandwith, no waveform information execpt amplitude and phase could be seen. You need at least threefold signal frequency to distinguish a sine wave from "not a sine wave", still without knowing the exact waveform.
Practically, if you are dealing with 100 MHz digital signals, you need 500 Mhz, better 1 Ghz oscilloscope to view signal quality parameters as overshoot and such.
Regards,
Frank