What conditions of 'Nushuz' (rebellion/disobedience) of the wife can be punishable by the husband?
If the conditions are applicable, how severe should the punishment be?

I have heard that punishment should not leave any marks nor can be hit on the sensitive parts such as the face.

If you can, please show us textual evidence of what I mentioned as well as the conditions of nushuz for applying this punishment of hitting.

Nushuz takes place if the wife:
1- Did not allow the husband to have relation with her, either by forbidding him from that, or putting barriers, such as keeping her self dirty, or with bad smell.
2- Leaving the house without his permission.
The punishment should go through three stages as you mentioned. However, beating (the last stage, and if he is sure that it works, and not makes it worse) should -as you mentioned- not leave any marks nor can be hit on the sensitive parts such as the face, and should be as minimum as possible, with the intention of putting the things in order, not as revenge.

فقه الرضا (ع): وأما النشوز فقد يكون من الرجل ويكون من المرأة، فأما الذي من الرجل فهو يريد طلاقها فتقول له: أمسكني ولك ما عليك وقد وهبت ليلتي لك ويصطلحان على هذا، فإذا نشزت المرأة كنشوز الرجل فهو الخلع إذا كان من المرأة وحدها فهو أن لا تطيعه وهو ما قال الله تبارك وتعالى: " واللاتي تخافون نشوزهن فعظوهن واهجروهن في المضاجع واضربوهن " فالهجر أن يحول إليها ظهره في المضجع، والضرب بالسواك وشبهه ضربا رفيقا،