Is it a condition to write details such as the deferred mahr (dowry) and the wife's work in the marriage contract, and can these conditions be demanded later if they were not written at the time of the contract?

A شرعي (Shar'i) marriage requires five elements: the husband, the wife, the wali (guardian, who directly conducts the عقد (contract) or delegates someone else, as a woman cannot do so herself), the إيجاب (offer) and قبول (acceptance), and two witnesses. If any of these five elements is missing, the contract is null and void.

Your agreement on the mahr (dowry) is your right, and it is not a condition for the validity of the contract that a part of the sadaq (bridal gift) be deferred. As for a woman's work and study, these are not conditions or elements of the contract. However, if they are agreed upon, then fulfilling them becomes obligatory, based on the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions."

Your eldest brother is the most rightful person to be your wali in marriage if your father or paternal grandfather is absent, unless his guardianship is forfeited for a legally recognized reason. Your stepfather is not among your awliya' (guardians). If he marries you off without your brother's permission, the marriage is invalid due to the absence of the wilayah (guardianship) condition, unless your brother authorizes him, in which case he acts as his agent.

However, if your brother has legally forfeited his wilayah, and there is no other wali, and your stepfather marries you off with your consent, then the marriage is valid in this case due to the absence of a wali and the Sultan, and a just man may marry her off with her permission.