Is it permissible to marry a second time without the knowledge of the first wife, to bypass statutory laws regarding polygyny, not to inform the guardian of the second wife that I am already married, and to marry with the following conditions agreed upon by the second wife: renouncing the right to childbirth, separation without consequences, renouncing the right to inheritance, and maintaining secrecy from the husband's family and acquaintances?

The husband is not obliged to inform his first wife of his marriage to a second wife, and he is permitted to proceed with the marriage on condition of maintaining justice between his two wives. If Islamic law permits polygyny, then any law prohibiting it is not to be considered. Caution must be exercised regarding anything that might lead to legal embarrassment.

It is not permissible to stipulate non-procreation, or non-claim of rights upon separation, or non-entitlement to inheritance upon death; these are void conditions.

There is no harm in stipulating that the marriage be secret, such that no one from the husband's relatives or acquaintances knows about it, and the wife must fulfill this, because it is a condition that serves an interest and does not contradict the essence of marriage.