Linux Licensing Question

I'm working on a research paper, and I need a bit of general feedback on something. As I understand it, most flavors of Linux are still free, but some of the bigger names now require payment if you're a business. So an individual can download Fedora, but a company has to pay for Red Hat.

Here are my questions:

1) Is that right? Or can a company, for example, download and install Fedora on a bunch of workstations without violating a license agreement?

2) If I want to run a server for a company, say to act as a file server, not for e-commerce or any kind of profit center, just infrastructure support, can I do that for free, or do I have to pay for it? (Assuming any distro -- doesn't have to be Red Hat.)

3) If I want to run an e-commerce center, to make major bucks for the company, does THAT copy of Linux have to be paid for?

I'm looking for specific licensing here, and while opinions are welcome, anything you can point me to that might have really specific legal information would be appreciated.

Thanks!