What is the ruling on a marriage that was documented in a German consulate in the presence of a judge and two non-Muslim witnesses, and without a guardian (wali), and what is the ruling on the children resulting from it, and what is the ruling on documenting the contract after fulfilling the conditions in Western courts?

Marriage without a guardian (wali) and witnesses is null and void by consensus (ijma'). The testimony of disbelievers is not valid in the marriage contract of a Muslim woman. Therefore, this marriage is invalid and must be renewed in the presence of a guardian for the woman (and if her guardians are disbelievers, then a Muslim judge or a just Muslim man shall marry her to him) and two just Muslim witnesses. As for the children from this invalid marriage, they are attributed to the man if the spouses believed the marriage to be valid. There is no harm in documenting the Islamic marriage contract in the courts of the disbelieving West.