If we format and re-install OSX through recovery, will it install the latest version? If we format and re-install OSX through Recovery Mode, will it download and install the latest version of OSX or use the existing version? I'm asking this because I noticed that it is downloading some files during the re-installation.
Have a look at the following links:

About macOS Recovery

How to reinstall macOS

From the latter link:


  Start up from macOS Recovery
  
  macOS Recovery installs
  different versions of macOS depending on the key combination you press
  while starting up. Hold down one of these combinations immediately
  after pressing the power button to turn on your Mac. Release when you
  see the Apple logo or a spinning globe.
  
  
  Command-R - Reinstall the latest macOS that was installed on your Mac, without upgrading to a later version.1
  Option-Command-R - Upgrade to the latest macOS that is compatible with your Mac.2
  Shift-Option-Command-R - Reinstall the macOS that came with your Mac, or the version closest to it that is still available.
  Requires macOS Sierra 10.12.4 or later.
  
  
  If you're selling or giving away a Mac that is using OS X El Capitan or earlier, use Option-Command-R to make sure that the
  installation isn't associated with your Apple ID.
  If you haven't already installed macOS Sierra 10.12.4 or later, Option-Command-R reinstalls the macOS that came with your Mac, or the
  version closest to it that is still available.