New Partition Read-Only

Most probably, you used an account with restricted access. It has nothing to do with GParted.
You have to log in as administrator and modify the access rights for this partition, to give full read/write access to everyone, or to the specific account you want.

Is this valid for all subdirectories too? Each folder and subfolder has his own permission menu.

I remember another issue with xp, with folders created and copied on a computer on an external drive. These folders were unaccessible on another xp computer, even from the administrator's account. To solve this, I changed the owner of the folders in the permissions menu for each folder separately (it took half a night to do this... ). I found that it was a known issue in xp. However, I can't think if this has anything to do with the problem you describe. Anyway, I remember several articles from (more or less) experts that explained why working with no full administrator privilege was't always possible under xp.