What are the wife's rights after divorce, knowing that the "shabka" (bridal gift) and home furniture are registered in her name? And did the husband and the girl commit a legal or religious error by writing an unregistered marriage contract? And does the second wife have any rights upon her divorce?

If you wish to separate from your husband due to harm he has inflicted upon you, or due to a defect that invalidates the marriage contract, you have the right to take the matter to court and request a divorce or annulment. In such a case, you would be entitled to all the rights of a divorced woman, including the mahr (both advanced and deferred portions, and the jewelry), the list of movable assets, and maintenance. However, if you seek separation merely because he married another woman, he is not obligated to divorce you, and he may refuse until you are compelled to seek khul'. Regarding the ruling on his marriage to that woman without the knowledge of her guardians, the majority of scholars consider this marriage invalid unless a judge rules it to be valid, or if they have followed the madhhab (definition) of Abu Hanifa. If he divorces her after consummation, she is entitled to her full mahr, even if the marriage is later found to be invalid.