Hey there,
Not sure why you are having issues with the Clock, is the BeatBuddy set to send clock? Check in your MIDI Out settings that nothing seems wonky (Press both Drum Set and Tempo knobs at once to go to menu, Main Pedal > MIDI Settings > MIDI Out)
as far as 2 goes, just go to Main Pedal > MIDI Settings > MIDI Out > Transition and disable the transition command coming out of the BB, this way you will never have the BB send a transition command to the Pigtronix, and the two will transition independently.
Also make sure you are either on 3.8.0, on the latest 4.0.1 version, or on 4.1.0 which is out on beta, 4.1.1 is coming soon with a small fix, if you do not use a MIDI controller to change parts 4.1.0 should work well for you!
You can verify in the menu what version you are on (About BeatBuddy in root menu)
Let me know!
Thanks for the question!