Make sure when you import the preset you import all triggers and settings! Sounds like an import issue
This is a super common question, I really need to add it to the first post in the release thread. There is an app-specific setting section in the BTT preferences window on the left side! There you can set apps to auto-disable BTT for.
That specific message about the calendar widget does not apply here, but you are correct that if you want to restrict what calendars show then you'll need to edit the widget. It runs a one-line shell script that calls icalBuddy. You can check out icalBuddy's resources, they're pretty comprehensive, and include how to call a specific calendar: https://hasseg.org/icalBuddy/
Reminders are also powered by icalBuddy, which lumps calendar tasks into reminders I believe. So if you have any tasks or todos in your calendar, my guess is that icalbuddy is sorting them as reminders.
@Andreas_Hegenberg question for you - is there a way to detect what Touch Bar group is open via AppleScript? I need to alter the functionality and highlighted state of menu bar buttons when entering and leaving their corresponding widget group.