I don't know how the license works. I might have to share the source code, but can I still sell copies of the game? And am I forced to make the source available to the public? Or does that only apply to modding the godot engine?
Yes, unlike the GPL you can distribute the binaries without having to share the source code. You will have to give credit where it's due though(by including the mit license verbatim to how its in the godot version used).