The method of nikah which you wrote will not make the nikah public, rather it would be a secret one, which is against sunnah, as it is asked in hadith to make nikah public.
عن عائشة قالت: قال رسو ل الله صلى الله عليه وسلم: أعلنوا هذالنكاح و اجعلوہ في المساجد ، واضربوا عليه بالدفوف (ترمذى:1/207? ابواب النكاح باب ماجاء فى اعلان النكاح).
In the same way, in the point number seven i.e. man is not responsible for livelihood (food, house etc), if nikah performed on this condition that husband will not be responsible for the maintenance of wife then it would this condition will be invalid being against the requisite of nikah. So, it will not be considered and the maintenance of wife will be wajib on husband. Imam Bukhari (رحمة الله عليه) has put regular chapter on the prohibition of such conditions:
باب الشروط التي لا تحل في النكاح
However, if wife forgives her maintenance right then husband would be free from it.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband