All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The woman's guardian (i.e. his presence and consent) is a condition for the validity of the marriage contract according to the majority of Islamic jurists, and this is the preferred view due to strong evidence. It is also the view that we hold here at Islamweb. Therefore, a woman cannot give herself in marriage, and so, this marriage is defective and it must be invalidated. For more benefit on the conditions of marriage, please refer to Fatwa 83629.
Nonetheless, the Hanafi School of jurisprudence is of the view that the guardian is not a condition for the validity of the marriage contract, and the country that rules according to this School of jurisprudence may rule that such a marriage is valid. However, as you know, the opinion of the majority of the scholars is the preferred one and it is not permissible for a Muslim to search for legal concessions to follow them.
Finally, we would like to draw your attention to the following matters:
1- Compatibility in the Islamic law is in faith; so consideration is not made for the material differences that you have mentioned. For more benefit, kindly refer to Fatwa 85252.
2- Announcing the marriage [and making it public] is recommended as we have clarified in Fatwa 39267, so it should not be concealed. Rather, some jurists are of the view that the marriage is void if there is complicity to conceal it.
3- If that man marries that woman without the knowledge of her guardian while he is aware that the guardian is a condition for the validity of the marriage contract, then he is sinful. However, if he does so out of following the opinion of the scholars who are not of the view that the guardian is a condition, then he is not sinful. For more benefit, please refer to Fatwa 130284.
4- That man is not obliged to reveal the identity of the two witnesses who witnessed this marriage.
Allaah Knows best.