Where do games install, and can I choose the folder?

Yes. When you install a game the launcher asks where to put it, showing the current folder, how much space the game needs and how much the drive has free. Pick another folder — a second drive, for instance — and that choice is remembered as the default for the next install.

Each game gets its own subfolder, named after the game. Moving that folder by hand afterwards is not supported: the launcher records where it put things, and will consider the game missing.