Yes, yes and yes.
I try to make changes in backgrounds in every cut, or at least changes when you cut between close-ups and totals. There are also changes within cuts, in order to describe the surroundings. The changes can be subtle, but the should in my opinion be frequent in order to keep the scene interesting to watch. It is good to have many tracks of material to build your backgrounds from, then you can easily make subtle changes, as well as more pronounced changes.
If you want to bring full attention to a specific element, it can always be a good idea to remove something else, including backgrounds.
I use spatial processing (do you mean reverbs?) whenever necessary. If for instance I have a sound of a car driving by in the street, but I need it to be further away, I will add some reverb and delay as well as decrease its volume, in order to make it sound right.