Yes — the core Corona framework is completely free, including Corona Native which can be used to extend Corona with native languages (C/C++/Obj-C/Java). There are no restrictions on which stores you can build for. Additionally, we offer a selection of plugins which allow you to easily extend the functionality of Corona; most of these are free, but some premium plugins must be purchased. Finally, the Corona Marketplace offers over 100 additional third-party plugins; many are free, while others are priced according to the vendors who maintain them.
Note — Apple, Google, and Amazon require that you join their respective developer programs to deploy apps in their marketplace(s). These programs have associated fees which you are responsible for.