If you're asking if the Preferences -> Measurement settings affect the number of displayed decimal places during or after taking a Measurement, the simple answer is no, those settings should not directly control displayed decimal places of the Measurement outputs. Those are controlled in Preferences -> User Interface under a couple of different areas.
Click on Preferences -> User Interface. The displayed decimal places output you see onscreen and NOT in the Information Window will be controlled by the number in the Dialog Box setting; the displayed decimal places shown in the Information window will be controlled by one of two settings - EITHER the System Precision in Information Window checkbox (which is 9 decimal places) or you can uncheck that box if checked and enter whatever number of places you want displayed in the Information Window setting (will be grayed out if you have the System Precision box checked).
The question in regards to if associative Measurement will update when you change units or displayed decimal places, YES they should update if you've put the Measurement at the end of your Model History. I don't usually use this feature so I cannot say for sure what happens when chunks of geometry are deleted and recreated - I will assume as long as there is a body or geometry present or part of the original body, you won't have any issues with the Measurement updating as expected. I only tested Measure Body since mass seems to be your main concern (nothing asking about distances, angles, etc.) and it updated when I changed my User Interface Preference for Displayed Decimal Places. Units also updated when I changed my Units under Analysis -> Units -> you pick 'em.
Finally, you're probably going to ask again what all those Accuracy and Tolerance settings are for in the Preferences -> Measurement dialog. Sorry, but I can't give you an answer that is useful or accurate. I've never worried about those settings since they were introduced into the software and have yet to have anyone dispute a body measurement I've supplied coming from a model on which I worked (I won't say how long it's been, but let's just say more than 5 years and less than 25 years - don't want to come off like I'm pounding my chest or that I'm an old fart). I also couldn't easily find anything in the documentation that outlined the effects of changing any of those values. For now, I wouldn't mess with them until someone else chimes in (like a Siemens employee or someone with equal knowledge as a Siemens employee).
Tim Flater
NX Designer
NX 9.0.2.5 Win7 Enterprise x64 SP1
Intel Core i7 2.5GHz 16GB RAM
4GB NVIDIA Quadro K3100M