Debian Hardware :: USB Stick Doesn't Seem To Be Partitioned?

I copied a couple of small files to it, and it seemed to copy fine, I was sure to unmount before removing, but those two files ended up being corrupted and although they appear on the stick, they can't be opened any more. Almost all the other files on the stick are still fine apart from one or two other ones, which definitely used to be openable but now are not. So perhaps it's got some bad blocks or something? So I hunted around for ways to check the stick, I'm guessing maybe it can mark those bits as bad and keep on using the other bits maybe?

I search, and I find fsck, so I run that on the stick and it doesn't seem to find anything, or complain about errors or anything, so I figure it's done nothing. (The stick is formatted as VFAT and can be read by both linux and windows). I remount the stick and see a new, extra file there, a deleted pdf from a few weeks ago apparently recovered by fsck. No problem, I delete it. But I guess that means fsck did do something after all. Then I unmount and remove the stick, and plug it in again just to check that things are working. And here's where it gets weird.

When I remount the stick, the files which were there before are no longer there. Instead, there's just a single png file, apparently from 2006, which I haven't seen since then I don't think. And I can open that file fine. Bizarre, where are my files gone? I unmount the stick, remount it, and all my files are back again! What the? Finding this curious, I run gparted on the stick to see if there is maybe more than one partition, and some glitch caused it to mount some hidden partition or something (I'm stabbing wildly in the dark, as you see). But gparted says that the whole drive is "unallocated", and fdisk seems to be saying it hasn't got a partition table. So I guess I've got a few questions coming out of this:

- Is this a problem that the stick doesn't seem to be partitioned? Should I partition it with gparted?
- Is there a way to do a proper check of the disk to check for bad blocks/sectors/clusters/whatever they're called, and mark them? fsck seemed to finish too quick to have really checked things properly.
- Is this stick dying and in need of replacement?