1. This depends on where you're buying from. For example, on the Kindle store, look at the "number of devices" restriction. If it says "unlimited", the book is not DRMed. DRM removal is pretty simple, but you'll have to go elsewhere to figure it out (hint: Google for "unswindle")
2. Not as such. Calibre will enumerate the books on your device if you plug it in, but otherwise Calibre has no way of knowing which book is where. You could add custom columns in Calibre and set them manually to indicate where the book is, but that's an entirely manual process.
3. Yes, Calibre stores files in its own "database" (which is just a filesystem structure, but don't go poking around in there -- let Calibre manage it). When you add a book to Calibre, it makes a copy. You can delete your original copy if you like.
4. Don't buy/download PDF "ebooks"? PDF is not a good ebook format. If the PDF is not DRMed (or you can remove the DRM), you can try converting it to a more suitable source (epub for Nook, prc/mobi for Kindle) but be warned that PDF conversion generally sucks. If you can get the book in any other format (epub, prc, lit, even plain text), you'll be much better off than trying to use/convert a PDF.