Haha, actually when I say handdrawn, it's my term for "made on the computer using only my own hands, as opposed to filters, layer styles, or any other computing algorithm, to make it.
For the sharp lines, I use two things to my advantge, the larger canvas and pixel brushes. Mostly the sharpness you see is due to the larger canvas. 512x512 looks even sharper. However, that will be lost on resizing so before you buy any head, you really should see the ingame version.
There are really pro artists here too. I just do this as a minor hobby. I have to look at something I draw for a while to break it down into colors and lines instead of entire objects. I think the longer you do it, the more experienced your eye gets, and the more patterns you see.
I started off way worse :]