Is it permissible for a suitor to see two sisters from the same family simultaneously, or to see one of them and then request to see the other if he is not pleased with the first, and what are the psychological consequences of that for the two sisters?

It is permissible for one who intends to propose marriage to look at the woman he wishes to propose to. It is also permissible to look at more than one woman, even if they are sisters, in order to choose one of them. If he sees a woman and she does not appeal to him, there is no objection to requesting to see her sister.