Thanks for all posts to refresh me, I don't own scope, but used scopes from 200MBW tek(DOS like GUI, poor waveform, Eth card costs me $668!) upto 50GHz Keysight. When I measure 16GHz differential signal I use 3.5mm CH1-CH3. I also tried 25GHz diff probe after calibration, yet it is a bit noisy - may be phase noise - to cause my measurement fail. Use 3.5mm/SMA I no need calibration.
BNC BW is 3GHz and well above 350-500M. Scope input has no divider but attenuator (except for OP gain change), for mv/Div ranges attenuators are bypassed or signal is directly passed.
Passive probe has its own capacitor compensation, traditional input cap is 13-15pf. That doesn't mean scope input cap. All low end scope (<=1G) uses simple relay to turn on 50ohm impedance if any, other than this, impedance matching (I mean signal path impedance) would be ignored, because path is short and is not 50ohm. The 50ohm is ended at the input to eliminate refection.
"Hires" as mfg stated is oversampling then "middle value filtering" (which is common is signal processing). "Average" is based on multiple trigging or samples average. Both can increase A/D EOB, which is also commonly used in SAR ADC.
I personally think the extra noise is more likely from ADC chip, yet shield input stage might help.
No doubt of 8GSa by interlaced sampling, or each ADC has 0.5ps delayed start pulse, I know FPGA can output calibrated delay line not sure whether can be so fine, I'm sure our DDR IP can, may be PCB/cable can, I use differential 3' cable pair with +-1ps tolerance. Many years ago HP 54601 scope uses "EQ" sampling, each capture can be shifted by 0.1ps, and real time sampling is only 10 or 100MHz (forgot)
5X is de facto std for sine wave, for example Keysight 3104T 1GBW has 5GSa, 16G PCIe signal needs 80GSa. Theoretically you can use Sinx/x and 2X+ sampling rate yet only when your signal is nice sine wave. 5X means each cycle you have only 5 samples, usually not enough for non-sine wave. So, 2GSa means you can use it for 400M signal, may be 500M sinewave.