He promised to marry her; does he have any marital rights
Question

                I have a female friend who got to know a young man; circumstances prevented him from proposing to her before he travelled, but he made a pledge that she is his wife before Allah and he intends to marry her when he comes back. Does he have any marital rights over her? Can he see her over the Internet without hijab?.
Praise be to Allah.The mere fact that your friend got to know this young man and he promised to marry her does not make her his wife under any circumstances. It is not permissible for him to see her and he has no marital rights over her, because the marriage contract was not done between them; rather she is a non-mahram to him. 
His saying to her, “You are my wife before Allah” is not correct, because she is not his wife, either before Allah or before the people. The marriage contract is not done with words such as this; rather it is essential that there be the proposal and acceptance, in the presence of her guardian and with his approval, and in the presence of two Muslim witnesses. 
So long as none of that has happened, she is not his wife. 
What this sister has to do is fear Allah with regard to her relationship with this man and others. It is not right for a Muslim woman to get to know young men who are not her mahrams, even if she likes their character or religious commitment, as she thinks. If he wants to marry her then he has to approach the matter properly, through his family and her family. In the answer to questions no. 36618, 23349 and 78375 you will find a detailed discussion on the ruling on forming relationships with non-mahram men and the ruling on corresponding with them. 
These relationships and haraam promises lead to nothing but evil and corruption. 
Many girls have regretted such relationships, but after a long time. 
Beware of falling prey to the snares of the Shaytaan. 
We ask Allah, may He be exalted, to protect us and you from all evil. 
And Allah knows best.