Thank you very much for the proper details and explanations, it helps me a lot. I have made a few modifications (I hope you don't mind), I will explain them below.
1. I believe you are looking for this exact configuration: https://i.imgur.com/2rxaCtG.png
These options will make sure that (1) at least one of the selected terms for each taxonomy group must match, (2) and that posts that are not marked with any of the selected taxonomy terms is excluded, and finally (3) if nothing is selected within a checkbox filter it is ignored.
Whenever the 'Open house' label is unselected, it is ignored (because of option 3), however when selected it is required to match (because of option 1).
2. You can actually do that by clicking on the display mode button, and adding a text and choosing the default. I did it for the 'property_type' taxonomy for you as an example: https://i.imgur.com/ksHXz8E.png
It results in: https://i.imgur.com/UJxUBPP.png
I hope this helps!Best,
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