Large gaps between home screen icons, can it be reduced?
AFAIK there's no built-in method to achieve that personalization.

I would go with Apex Launcher by Android Does available from Google Play Store, to use with Android 4.0+, it's free and among the features you'll find:


  
  Customizable homescreens and grid size
  Scrollable dock
  Infinite &amp; elastic scrolling
  Customizable app and folder icons
  Multiple drawer styles
  Drawer apps sorting
  Hide apps from the drawer
  Enjoy homescreen gestures
  Backup/restore settings and data
  


APEX Launcher Homescreen Settings:



Other features can be found if you go PRO.