Natural Docs is licensed under version 3 of the GNU Affero Public License, or AGPL.
This means that Natural Docs' source code is available and you're free to use and modify it. However, if you distribute a modified version of it, or use its source code in another project, or build a service incorporating its functionality, then that project or service's source code must also be available and licensed under the AGPL, giving other people the same rights I gave to you. Note that this does not apply to your project if you're only using Natural Docs to document it.
If you're only using Natural Docs to document your project, its license does not affect yours. You can still license your project under any terms you want, and you can distribute documentation generated by Natural Docs with it as well.
It's only if your project incorporates Natural Docs' source code into it or you build a service that incorporates Natural Docs' functionality that your project will become bound by the AGPL. Simply documenting it with Natural Docs and distributing the generated files will not cause this.
The generated documentation as a whole is not bound by the AGPL. You can distribute it under any terms you like.
Yes, though it would require a paid support contract. If you wish to license Natural Docs under different terms please contact Greg Valure.