Can you take purely mental actions while stunned? I know the description says no actions, but paralysis which is supposed to be a "stronger" effect seems to allow them, so I thought I'd clarify that.
As for Stunning Fist, if your attack hits, but you do not deal any damage due to DR, the enemy does not have to save at all right?
Thanks in advance.
No, you cannot act when you are stunned. You're right, paralysis allows for mental actions, but this is explicitly stated in the Paralysis condition. There is no such explicit exclusion in the Stunned condition, an the Stunned condition does explicitly state that you cannot act, therefore no such exlusion is allowed by RAW; if you are stunned, you cannot act.
Maybe think of it this way. Paralysis affects just the body. The mind is still alert and capable (for most of us, that isn't saying much, but for psychics, psionics, and some other kinds of magic-users, that can be saying a whole lot). But stun affects the nervous system, including the brain, shutting it all down while the condition lasts.
As for Stunning Fist, the description (see the Feat) specifically says "Stunning Fist forces a foe damaged by your unarmed attack..."
So you are correct, if there is no damage, then there is no stun and no need to save against stun that doesn't exist.
I don't know about paralysis being 'stronger' per se, just different. Being stunned includes mental actions. The paralyzed condition specifically points out that purely mental actions are permitted.
So no, a stunned creature cannot take any actions at all.
If an effect deals no damage then any secondary effect from that attack is not applied.
*edit* ninja'd by a tarrasque? WTF?!? ;p