Is it valid to renew a marriage contract that was concluded without an authorized شرعي (Islamic legal) marriage official, and with the testimony of non-عدول (pious and upright) witnesses, while waiving the mahr (dower) before it was specified, and without recalling the صيغة الإيجاب والقبول (formula of offer and acceptance) or استبراء الرحم (ensuring the wife is not pregnant from a previous marriage)?

It is not a condition that the marriage contract be officiated by a ma'dhun (marriage officiant). If the offer and acceptance take place between the guardian and the husband or his representative, and witnesses attest to it, the marriage is valid. The uprightness of the witnesses is a condition according to the most authoritative opinion. Doubt concerning the offer and acceptance after the contract has been concluded is not to be heeded. Everyone present at the contract signing is considered a witness, except for the guardian. Not mentioning the mahr (dower) at the time of the contract does not invalidate it. If she waives it before the contract, it is not forfeited. If she waives it after the contract, it is forfeited.