I don't know about the window (I will look at that later) but you may want to try saving the geometric properties as an expression and work with them from there. Expand the menu and look for the associative check mark.
The decimal places in your information window can be changed in your Customer Defaults. There are two places for the different units.
File (pull-down) > Utilities > Customer Defaults > Gateway
The picture is actually wrong, I am not showing the two places (units) to change them, but you can see where to change for millimeters and you can probably find the inches from there.
I have set the dialog box decimal places to 6, Info window to 12, and tracking bar to 4. Unfortunately the geometric properties dialog results still appear as 3 place decimals.
If you changed your Customer Defaults, it won't take effect until you restart NX and create a new file.
Before you restart, try changing the settings under Preferences -> User Interface -> Options (on the left) and make sure the dialog is fully expanded and you should find entries for all 3 items. If Use System Precision is checked/ticked, un-check it and enter 12 if that's how many decimal places you feel is required.
I have a feeling that the geometric properties dialog box is hard coded for 3 decimal places and won't be affected by any of the above options. I don't think you can adjust the number of decimal places for this particular dialog.
I suggest contacting GTAC and opening an incident report (IR), if what you want is possible, they will tell you how to change it; if it is not, your IR will be turned into an enhancement request (ER) for possible inclusion into a future version of NX.
I also believe it is hard coded to (3) places. Another very limiting aspect is it seems to also be hard coded to use absolute and does not recognize the WCS locaton and orientation.
A while back Siemens was talking about discontinuing Geometric Properties and when I asked a dev about it, he wouldn't or couldn't say what the replacement was. Geometric Properties is an extremely valuable tool for many users so I sincerely hope they do not discontinue it but I hope a lot more that they improve it or even replace it with a better tool.
Another feature that should be added to it is dynamic slope analysis. The current slope function works great but is too cumbersome to use for quick checks, not to mention is separate from the Geometric Properties dialog. Some mid-tier cad/cam software, such as Mastercam, have had it for years.
For the record, I'm talking about the "results" section of the geometric properties dialog box when you do a "dynamic" analysis and drag the cursor over a face; the results here seem to be fixed at 3 decimal places. Perhaps I misunderstood the question; if so, sorry to add to the confusion.