Is it Islamically permissible for a Muslim man to marry a Muslim woman by her appointing a Muslim brother as her guardian (wali) in the marriage contract, in the presence of two witnesses, with a written contract signed by the two witnesses, especially since she has no guardian in the country of residence, and for a triple divorce to be pronounced at the wife’s request?

For a valid Islamic marriage (nikah), there are conditions, one of which is the guardian (wali). If a woman does not have a Muslim guardian, then her guardian is the Muslim ruler (Sultan) or his representative. If these are unavailable, she can appoint a righteous Muslim man to marry her off. If the woman does not have an accessible guardian or a Sharia judge, then her appointment of a Muslim man is valid, and her marriage contract is valid. However, if she has an accessible guardian or a Sharia judge, then it is obligatory to contact the guardian or to authorize the judge to conduct the marriage contract. In this latter case, the marriage is not valid. If you were ignorant of the ruling, you are not sinful. And for divorce, merely uttering it is sufficient.