Praise be to Allah.
In order for the marriage contract (nikaah) to be valid, it is stipulated that it be done in the presence of the woman’s guardian (wali) or his proxy
In order for the marriage contract to be valid, it is stipulated that it must be done by the woman’s guardian or his proxy. If she does not have a guardian, then the shar‘i judge (qaadi) may do the marriage contract for her. If there is no shar‘i judge, then the director of the Islamic centre, or an imam or a Muslim man of good character may act as her guardian.
Ibn ‘Abd al-Barr (may Allah have mercy on him) said: If the woman is in a place where there is no Muslim authority and she has no guardian, then her affairs may be handled by a trustworthy neighbour of hers, so he may do her marriage contract, and he will be her guardian in this situation, because people have to get married, and they should do that in the best way possible.
End quote from at-Tamheed (19/93).
Ibn Qudaamah (may Allah have mercy on him) said: If the woman has no guardian and there is no Muslim authority, then there was narrated from Ahmad that which indicates that a man of good character may do her marriage contract for her with her permission, as he [Ahmad] said regarding the headman of a village: he may do the marriage contract for a woman who has no guardian, if he has checked for her the matters of compatibility and the mahr, if there is no judge (qaadi) in the village.
End quote from al-Mughni (9/362).
There is nothing wrong with your father doing the marriage contract if he is of good character.
Stipulation of witnesses to the marriage contract
The majority of scholars are of the view that it is stipulated that the marriage contract be witnessed by two Muslim men of good character in order for it to be valid, except that the Maalikis were of the view that having the marriage contract witnessed is mustahabb (recommended), so it is permissible to delay the witnessing until closer to the time of consummation, and it does not have to be at the time of drawing up the marriage contract. If two Muslim men testify before consummation of the marriage, it is valid.
Ad-Dardeer said: It is recommended to have two men of good character witness the marriage contract. One who is not proven to be of good character, either because his character is unknown or because he is an evildoer, is not valid (as a witness). The witnesses should be other than the guardian, who is the one who has the authority to do the marriage contract; even his proxy cannot act as a witness to the marriage contract. This is why we said it is recommended (to have two witnesses). As for having witnesses before consummation of the marriage, that is obligatory and is stipulated.
End quote from ash-Sharh al-Kabeer ma‘a Haashiyat ad-Dasooqi (2/216).
Some of the scholars are of the view that it is not a condition to have the marriage contract witnessed; rather it is sufficient to announce the marriage, and when the marriage becomes widely known and is announced, it becomes valid. This was narrated from Ahmad (may Allah have mercy on him).
It says in al-Mughni: Ibn ‘Umar, al-Hasan ibn ‘Ali, Ibn az-Zubayr, and Saalim and Hamzah, the sons of Ibn ‘Umar, did that.
It is also the view of ‘Abdullah ibn Idrees, ‘Abd ar-Rahmaan ibn Mahdi, Yazeed ibn Haaroon, al-‘Anbari, Abu Thawr and Ibn al-Mundhir. And it is the view of az-Zuhri and Maalik, if they announce the marriage. Ibn al-Mundhir said: There is no proven report about the two witnesses to the marriage contract being a must. End quote.
This view was favoured by Shaykh al-Islam Ibn Taymiyah, and was regarded as more likely to be correct by Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him). See: ash-Sharh al-Mumti‘ (12/94).
Shaykh al-Islam (may Allah have mercy on him) said: Undoubtedly if the marriage is announced and made known to people, it is valid, even if it is not witnessed by two witnesses. But if it is concealed and limited to the witnesses only, this is subject to further examination.
If it is witnessed and is also announced, there is no dispute that it is valid.
If it is neither witnessed nor announced, then it is invalid according to all scholars, and even if we assume that there may be some who differ, they are very few.
End quote from al-Ikhtiyaaraat al-Fiqhiyyah, p. 177.
What you have mentioned about the witnessing of two men concerning whom you are not certain whether they are Muslim, let alone whether they are of good character, their testimony is not valid; rather it is essential to verify the character of the two witnesses, so as to dispel ambiguity about their character, and then confirm whether they are Muslim and of good character.
Ibn al-‘Arabi (may Allah have mercy on him) said: If he wants to have the marriage contract witnessed, he should get two men of good character to witness it, who are the kind of people on the basis of whose testimony what is due to people could be confirmed.… This was stated by the scholars of Islam.
End quote from ‘Aaridah al-Ahwadhi (5/19).
The way out from this dilemma is to bring two witnesses of good character to testify, then the marriage will be valid, according to the Maaliki madhhab.
Or you can announce the marriage – if you did not do so already – then offer a wedding feast, and invite people to celebrate your marriage, and the like, then the marriage will be valid.
But to be on the safe side, you should repeat your marriage contract, in the presence of the guardian who has the authority to do the marriage contract, namely your father, as you mentioned. And it should be witnessed by two Muslim men of good character, then the marriage should be announced to the people around you, as noted above.
Doing the marriage contract through social media
It is valid to do the marriage contract through social media, on condition that you are certain of the people who are party to the marriage contract and the witnesses, and you are sure that it is unlikely that any deceit or cheating will occur.
This has been discussed previously in the answer to question no. 105531 .
And Allah knows best.