Are the conditions set by the wife (performing Umrah before the second marriage and not having children in the future) for her agreement not to seek Khul' valid conditions in Islam, and is it permissible for the husband to agree to them?

A woman is not permitted to seek a divorce (Talaq) or annulment (Khul') except for a legitimate Shar'i reason, such as the husband's ill-treatment or fear of not fulfilling his rights. Otherwise, she is sinful. A man marrying another woman does not entitle the first wife to seek an annulment unless it causes her unbearable hardship that prevents her from fulfilling her husband's rights. It is permissible for the wife to agree with her husband on compensation for his marriage to another woman, but this does not obligate him, nor is it conditional upon her permission. Procreation is a shared right between spouses. It is not permissible for a woman to stipulate not having children in exchange for her remaining married or fulfilling his rights, unless both agree. The husband should weigh the benefits and harms if the wife rebels.