Originally, I downloaded and installed Unreal Launcher and then Unreal Engine (4.19). Then I built Unreal Engine from source. I am wondering if I need to keep both the launcher and/or the pre-built engine?
No, if you get the source version you can just run with that, but its nice to have the launcher. You do have to have the launcher if you plan to add marketplace content, like plugins, assets, or unreal studio. as that is the distribution channel for that content.