Praise be to Allah.
It is valid to do the marriage contract via video phone, and it does not matter if the woman is not seen; it is sufficient to hear her voice, if there is no risk of mischief.
Please see the answer to question no. 105531.
In order for the marriage contract to be valid, it is stipulated that it be done by the guardian (wali) of the woman or his proxy; the woman should not do the marriage contract or appoint a proxy for it. This is the view of the majority of scholars, with the exception of the Hanafis.
The marriage contract that is done by a proxy appointed by the woman to do it on her behalf is only valid according to the Hanafi madhhab.
So long as the marriage contract was done according to an established madhhab, it is not to be invalidated, especially since it is known in this case that the father agreed to the marriage and was in fact present when the marriage contract was done.
In order for the marriage contract to be valid, it is essential that the marriage contract be witnessed by two Muslim witnesses, and it is not valid for the guardian (wali) to be a witness.
It says in Sharh Mukhtasar Khaleel by al-Kharashi (3/168):
It is not permissible for the wali to be a witness to the marriage contract of the woman under his guardianship, even if there is someone else with him (as a witness). End quote.
See the answer to question no. 194435.
In that question we pointed out that testimony is not limited to those who are asked to be witnesses and sign the official papers; rather anyone who is present when the marriage contract is done and is fit to give testimony is a witness.
Based on that, the imam of the mosque in this case may be considered a second witness, and the marriage contract is valid; it does not matter that he was acting as registrar.
Moreover, it is valid for the brother of the wife to be a witness to her marriage; there is a difference of scholarly opinion as to whether it is valid for her father to also be a witness.
It says in Sharh Mukhtasar Khaleel by al-Kharashi (7/180): The apparent meaning of his words indicates that it is permissible for a brother to give testimony for his brother, whether in the case of deliberate injury or otherwise, and whether his testimony will raise his brother in honour and status or not, or whether it will ward off harm from him or not… The words “whether his testimony will raise his brother in honour and status or not” refer, for example, to his testifying that he married someone by marriage to whom he would gain honour and status because of her being an honourable woman. End quote.
See the answer to question no. 215137.
The marriage contract is valid, praise be to Allah.
And Allah knows best.