Is it permissible to marry a woman who declared her conversion to Islam for the sake of marriage, but stated that she would not wear the hijab and would not pray? And to what extent is it permissible to marry a second wife when there is a cooling in the existing marital relationship?

Familiarity between foreign men and women is a door to temptation and corruption, especially with a non-Muslim woman. What is incumbent upon you is repentance and severing your relationship with her. If you wish to invite her to Islam, let it be through a mahram. You must be frank with your wife to understand the reasons for the cooling of your relationship and how to remedy it, knowing that establishing a relationship with a foreign woman is one of the causes of waning feelings towards your wife, and the ill-omen of sin reduces blessings. If your repentance is sincere, Allah may set your affairs aright for you. If you need to marry, then choose a Muslim woman of religious commitment, acting upon the recommendation of the Prophet, peace and blessings be upon him: "So, choose the one who is religious, and you will prosper."