Let's say I plan to buy a used PlayStation 3 without a box, how can I tell how big the hard drive is?
Unfortunately, you'll have to take the word of whoever is selling you the system. If it's GameStop or some other local used game retailer, chances are they'll let you boot it up in the store to check the listed drive space. Remember, though, that the HDD is easily upgradeable, so you may want to go ahead and buy a 2.5-inch drive and install it yourself.
How do I go about replacing the disk drive in my PS3?
There's a great tutorial, with pictures, right here.
Why do some systems have full backwards compatibility, some partial, and some no compatibility with PlayStation 2 titles?
You can find a more thorough explanation here, but the gist is internal hardware: the initial PlayStation 3 consoles (20GB and 60GB) shipped with the core PS2 components -- the CPU and GPU -- and as such functioned as a PS2 for emulation. Hence, full backwards compatibility.
The 80GB model (and 60GB model for PAL territories) did not include the PS2 CPU and instead had written software that relegated the Cell processor to handle CPU duties. (The GPU remained within the system.) The process isn't perfect and there are hiccups, but it does play most PS2 games.
The 40GB model eschews the PS2 hardware entirely but does not include software for emulating the GPU. Therefore, no PS2 compatibility whatsoever.
What about PlayStation One games?
PS One games are backwards compatible on all versions.
How can I determine that backwards compatibility on a used, unboxed system?
The 20GB model doesn't have the chrome trim (and also lacks a flash card reader), so you can be guaranteed backwards compatibility with that one. On the other end of the spectrum, the 40GB only has 2 USB 2.0 ports, so you can tell which model has no PS2 backwards compatibility.
If you want to get picky, however, another way to do is by checking the model number, located on the bottom of the console (see picture below). The fourth letter defines the model - for example, in the picture below, CECHG01, represents the 40GB model and therefore has no PS2 compatibility. "A" (60GB) and "B" (20GB) have full compatibility, and "E" does compatibility via software emulation.
Isn't answering questions you posed to yourself a bit schizophrenic?
Who am I answering?
Just don't tell me to burn things.