New to Linux and starting with Manjaro. Trying to wrap my proverbial mind around it! 30 minutes in and I’m getting a “502 Bad Gateway” error trying to install new software. Not a good start!
Hi and welcome 
The users of this forum can help you, we need some more info where this error is generated, this might be a issue with mirrors or a network configuration adjustment. Please read this excellent thread how to help the forum users help you better:
A quick try is to generate your mirrors again, this can be done in the add/remove software application (pamac) under settings or from a terminal running sudo pacman-mirrors --fasttrack && sudo pacman -Syyu
There is some lack of detail were are you getting a 502, I am going to assume you are clicking the link in manjaro hello, if so you can head to software.manjaro.org and install from there or open add/remove software from your apps menu.
That was already fixed with manjaro-hello 0.6.7-5 last week. 