I took a quick glance at both files you attached. Which doctor or command were you running when you got the first set of errors about gparted and such? That was strange indeed. Curious that it is referring to the gparted partition manager which handles setting up the flash storage on the TP, so it sounds like it's in the same ballpark as where the rest of us were.
On the other hand, the better news is that the second set of messages you attached actually look almost identical to those that I've seen before with myself and a few other folks who had this problem.
The short story in my case was that the doctor I was running must not have downloaded properly, and after just redownloading it again from the web, everything worked a charm. Lucky me.
For a lot of others, the problem was with a small glitch in the flash storage on the TP, which was fixed using the "dosfsck -r /dev/mapper/store-media" command on the TouchPad itself (NOT on the computer) over a novaterm connection. What I mean by that is that after your doctor has failed at 12%, you can run the "novaterm" command from the linux command prompt on your PC, and it will take you to the command prompt INSIDE the TouchPad itself. From there, you run the "dosfsck -r /dev/mapper/store-media" command. Afterwards, type "exit" and try running the doctor again.
If THAT doesnt work, I would suggest running the commands to rebuild the flash storage structure altogether (btw, this will erase everything currently saved on your TP).
Here are the steps:
-after the doctor fails at 12%, run the "novaterm" command from the linux command prompt on your PC. This will access the command prompt of the TP itself.
-from that command prompt, run "lvm.static vgscan --ignorelockingfailure"
-then run "lvm.static vgchange -ay --ignorelockingfailure"
-then run "mkdosfs -f 1 -s 64 /dev/store/media"
-then, type "exit" and try running the webOS doctor again
Between redownloading a fresh doctor, repairing the flash storage, or rebuilding the flash storage, you should be able to resolve this.
Side note: I suggest using a copy of the newest webOS 3.0.4 doctor during this whole endeavor.