What is the religious ruling on a wife remaining with a husband who claims to be religious, but then she discovers he watches pornography, mistreats her, and refuses to divorce her or grant her a Khulʿ?

If the husband watches pornography, you should advise him gently and kindly, reminding him of Allah and His punishment, perhaps he will repent. If he persists in his transgression, you may request a divorce. If he does not respond, then refer the matter to Islamic centers to remove the harm through divorce (talaq) or khula'. You also have the option of being patient and continuing to advise him. As for his desire to marry another woman, this is permissible for him if he is capable of being just, and you do not have the right to object or request a divorce for this reason, unless you had stipulated that he not marry, in which case he must fulfill the condition. If he does not fulfill it, then you may request a divorce.