Trigger "Bug":
The Keysight scope is using the traditional Auto trigger. It just triggers automatically and displays whatever is sampled during the sweep period. that is normal operation. Some scopes use what's called "Combination Trigger." It triggers a sweep automatically, but if it finds something during the capture that fits the currently set trigger criteria, it will retrigger at that point. Not all scopes do it, and some people don't like that type of trigger operation. Auto trigger is really meant to help find a signal and set the trigger, then switch to "Normal" trigger for operation.
Waveform Performance When Scrolling Horizontally:
Think about it, if you are displaying the waveform 3-4ms before the trigger, the scope must capture the waveform from that point up until the trigger point at least. So, you are effectively slowing down the capture rate.
Sample Rate Affected By Number of Channels Enabled:
Traditionally scopes sample the channels in pairs. 1 & 2, 3 & 4. TEK may be doing something different by routing the signals to unused ADC's, but that is unusual. Even a 2 channel scope will reduce the sample rate by 2 when both channels are on. A 4 channel scope is really just two, 2 channel scopes in one box. So, once again, it is normal and expected that using channels 1 & 3 will maintain full sample rate.