How to prevent browser from redirecting AT ALL using terminal I have a very limited knowledge of this stuff so I hope this explanation makes sense....

My parents have somehow got on my MacBook, and made it so that they can change any setting and view/modify my or their own internet traffic. They can achieve all this from upstairs. And their modifications aren't always "live", ie: modifications in real time. 

Sometimes the screen 'glitches' and I see something that is non standard, ie: some web error flashes up on screen when I try to load a certain page, before reverting to the usual 404 not found page.

Oh and my 2016 MacBook Pro thinks it's up to date and it's running OS is 10.3.3 

I believe all my internet traffic is being run through a homemade proxy which is how they achieve evil tyrant overlord status.

If someone could help me restore the MacBook to out of the box factory settings, whose installer verifies itself that it is authentic apple software by communicating with apple servers, I'd be very grateful.

Thanks
My parents have somehow got on my MacBook, and made it so that they
  can change any setting and view/modify my or their own internet
  traffic.


At a very minimum, this is a function called (Apple) Parental Controls and they are working exactly as designed.  There are also tons of other 3rd party control/monitoring applications that do exactly this.  


  I believe all my internet traffic is being run through a homemade
  proxy which is how they achieve evil tyrant overlord status.


If all your network traffic is being run through a proxy/firewall/content gateway, you won't be able to bypass it especially if it's an all-in-one device like a pfSense gateway.


  Oh and my 2016 MacBook Pro thinks it's up to date and it's running OS
  is 10.3.3


It indicates it's up-to-date, because it is up to date.  There's nothing "non-standard" about your install of macOS.  


  If someone could help me restore the MacBook to out of the box factory
  settings...


There are many tutorials on this site and on the web in general on how to restore macOS to factory settings.  However, I'm refraining from answering in this context because this is (appears to be) your parents' computer and network and there is one fundamental rule that we as professionals abide by:

Their Network = Their Rules


Whether it's your parents or a network admin at your place of work, going around them won't do anything to win their trust.