"I saw Othello's visage in his mind" The sentence with "visage" is significant here; it can mean "subsumed Othello's foul face in his fair mind" or " "saw Othello as he saw himself." If we take the first interpretation to be correct, what does this imply about Othello and Desdemona's union?

This is an interesting question. These words are spoken by Desdemona to the Duke of Venice at the beginning of the play, in explanation of the marriage which has just taken place between Othello and Desdemona. The duke is asking Desdemona to clarify the situation. Desdemona has asked for the duke's help; she wants to explain herself and convince the gathered assembly that there has been no coercion between them—that is, that she loves Othello.
So, when she says, "I saw Othello's visage in his mind," I would understand this to refer back to "the very quality of my lord" in the previous line. Effectively, Desdemona is saying "I saw the real Othello—the true quality of him and the heart of the man—through his words and actions, his thoughts and feelings as he expressed them to me." However, the use of "visage" could seem particularly significant because Othello's visage, or face, is markedly not the same as the faces of the other people in the scene. It is thought so shocking that Desdemona should love Othello because, unlike everyone else in Venice, he is black.
What might this imply, then? Arguably, these words could be understood to mean that Desdemona was able to overlook Othello's blackness, his black face and "thick lips," because she was able to see beyond them to the man inside. You could potentially make the argument that she's saying she sees his real face as a white one. But does this reflect on their marriage itself?
1. If Desdemona really means that she doesn't see Othello's black face because she sees beyond it to his true "visage," this would imply that she's as repelled by his blackness as everyone else, to a certain extent—or at least that she doesn't want to think about it and thinks less of him for it. Is this borne out by the play, though? I would argue that it isn't—Desdemona certainly respects Othello as her husband.
2. We could argue, however, that Desdemona knows what everyone else in the room is thinking and loves Othello so much that she wants to manipulate them to get her own way, so she and Othello can be together. What if she's trying to put their minds at rest by using this language? She may be saying: "I know what you're all thinking—he's black. But that doesn't bother me because I don't really see that when I look at him; he is of such good "quality" that he almost appears white to me."