I personally use linux, because that's what's hosting my site, but it's certainly not mandatory. It may make some things easier, but probably not :)
I think the main thing to remember is that file names are case sensitive on linux, but not windows, and that can cause errors if you're not expecting it.
As for editors, I assume you mean HTML editors? There's nothing set by default, it will depend on which distribution you use (ubuntu, redhat, etc.). And you'll likely have to download something yourself.
I personally have used Nvu and Quanta. They're not as good or easy to use as Dreamweaver or Frontpage (my personal opinion).
I'd also recommend Nvu if you're familiar with FrontPage but are using a Linux OS. It's free of cost and can upload files using the built-in FTP manager. If you don't need a graphical editor, I'd very much recommend vim. :-D
vim all the way! If it's configured with syntax hilighting and search hilighting, and you can get used to the commands, it's the best ever for command line html/php/any scripting language you can think of.
There are some great quick reference materials out there. This isn't the easiest one to read, but it's one of the most complete:
The default text editors at the linux command line are usually vi and/or nano (or do they call it pico these days...?) Emacs is also an excellent choice, but it's so huge and clunky in my experience... Nano/pico is probably the easiest to use, but doesn't do syntax hilighting very well.