Is it possible to make a Custom Launcher to automatically update the game to the latest version?

I would take a look at this link here You will for sure need to have a standalone application to patch the game, you could also consider having a way to patch the patcher as well, which you may not need.

Is it possible and if so, how, to make a launcher for the game that will check online to see if your version is the most up to date, and if not update the game for you.

I have some experience in c++ if that helps.

Thanks or your time