The title essentially describes the problem entirely, but the copy option for the selector also does not copy the attached physics components.
#[unstable] Cut & Paste objects with physics components neither cut nor paste the attached components
limpid adder
clear condor
Post a video of what’s happening so they can better reproduce it
clear condor
Box mode only works on one grid at a time.
On keyboard, you can hit enter to add the current box to your selection, but I don’t see that option for controller (looking at the bottom left hints). Maybe it’s missing 
scenic knot
I wonder if there's a way this could be visually communicated, like if physics objects within the box selection could be rendered on top of the box or somethin.
(though I guess that kinda does happen, when you copy it the copied part turns blue)
Maybe physics objects entirely within the box selection could be included in the selection, which is more intuitive, but probably less exact
maybe it could be an option in the settings that's on by default