Hey Drew.... where did you find Fusion 360 for free? The only thing I've been able to find on it is a trial version. The trial version won't allow for saving/exporting the file(s), nor can you actually use the files you create without purchasing the software. OK, spill the beans....what do you know that I don't about it?
It's been a while, so I don't clearly remember, but after my trial version expired, I seem to recall it gave me an option to renew/continue, and I just went ahead with it. At first it seemed like it was going to make me pay, but if you go through prompts, it will renew without needing any payment info if you're claiming use as a hobbyist. From what I understand,even the "business" license is relatively cheap, but you don't need that unless you're making over a certain amount of money (100k or so I think).
As for saving files, I don't believe you can save them locally, just through their cloud based storage, which at first I found annoying, but it's actually a little more convenient once you get used to it. If you want to share files, there's a way to do that through links and what not, I believe, or you just log into your account from another computer with Fusion installed on it.
Now, for exporting files to Mach 3, or some other CNC or CAM based software, I haven't quite gotten to that point yet, but I know of plenty of guys that are doing it, and there are a number of youtube vids about it as well.