If I undestend you correctly, you need to use actions ToggleSelect in your buttons instead of Select. That is:
For button Q1 - action ToggleSelect, field Quarter, value Q1
For button Q2 - action ToggleSelect, field Quarter, value Q2
Toggle select does changes selection of one value, without clearing other values.
Second question is leess clear, and the attached application is empty, so i can't guess...