For the first question Preferences>Visualization and under the Colur Palette tab Edit Background. There you can select either plain or graduated display and choose the colors you prefer. Setting this will affect the work part only but will be perseistent for that part. To change the background display for all existing parts is more difficult, perhaps the best way is to create a macro and run it as needs be.
To change all future parts one would need to both edit the customer defaults File>Utilities>Customer Defaults, provided you have permissions to make such changes. That would take care of some new parts but many are templated off saved template files and nullparts that the system uses. In addition to those there are seperate null files for several of the translators in inches and metric versions that we also tend to replace with our preferrred versions.
Moving components within asemblies is done by repositioning them using Assemblies>Components>Reposition Component, or more usually the icon. Fortunately the pull down menus also display the icon so once learned most users customise their standard toolbar settings and save roles with these frequently used functions available.
Moving geometry within a part file that does not involve components is done using transformations. This changes between NX-5 and NX-6 so a detailed explanation is best drawn from the documentation.
Assemblies also make use of mating conditions or latterly assembly constraints which in many cases is easier than repositioning.
Like any system sometimes we work with translators between different software, so when as all possible and as far as can be appropriate many users prefer to model the majority of components for any given design around a common absolute co-ordinate location. In this way imported/exported data via any translator will always arrive in the correct assembled location. It may be worth considering this impact when deciding whether to reposition or mate via assemblies at random or to apply transformations within the part geometry to position it.