I'd like to use GUI0 for my own purpose but I'm not sure it hasn't any special built-in particularities that I don't know of.
I've been looking in the manual, and also on the forum (keyword : GUI0), but haven't found anything relevant.
Do you know anything about it ?
You mean the STATUSLINE gui in the default template? AFAIK it's only referenced in this template script, if at all. It isn't used by any AGS internals and you can safely delete it.
Even the INVENTORY gui is just a template that can be deleted if it isn't used in your script. It just happens to look like the built-in one that's called by the InventoryScreen() function because that one can't be modified.
Edit:
However, be aware that the sprites of the INVENTORY template gui are also used by the internal one, so don't delete those!