Where is the save-data adapter?

You need to add it to the folder via the add-item drop-down.

A mailer adapter is in the "sample" form created when you add a form folder because it's probably the most common use. Other adapters need to be added.

Why are these action adapters content types? Why aren't they just built into the form folder?

There are several reasons. One is that doing it this way makes it easy to copy configured action adapters from one form to another.