Is it possible to reinstall MacBook firmware?
Do MacBook devices have something [firmware] similar?


Yes.  It's call the EFI or Extensible Firmware Interface


  Is it possible to reinstall MacBook firmware?


Yes.  See this post:  Where is the EFI stored on the macbook and is it possible to restore a previous EFI firmware version?


  Is the firmware automatically reinstalled upon an OS reinstallation?


Not necessarily.  The EFI is upgraded only if it needs to be upgraded.  This can happen as part of a normal update process or it can happen as part of a macOS installation.    

From Apple Support:


  Most firmware updates are automatically installed when you update or
  upgrade OS X. Some firmware updates are also available as downloads
  you can install manually. If your Mac needs a firmware update and it
  isn't installed automatically, check to see if a manual updater is
  listed below.


For the record - upgrade is defined as going from one version of macOS/OS X to the next one up.

It also goes on to state (which they highlight) the following:


  If you don't see a firmware version listed in this article, it means
  that either a firmware update is only available as an automatic
  update, or no firmware update is needed.