All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There are many ways to look for a wife in Islam. For instance one can make inquiries through his female relatives or by asking male friends to query their female relatives on his behalf. If he learns of one or more women, he has to make Istikhaarah (to pray two optional Raka'h) seeking guidance in making a decision or choosing the proper course of action. He should also seek the advice of those who know each one of these women. If he feels in his heart that he is attracted to marry any of them, there is no harm in his looking at her with the presence of one of her Mahaarim (non-marriageable relatives) or at a gathering so that he would not be in seclusion with her. The Prophet said: ''If one of you proposes to a woman, there is no prohibition in his looking at (some parts) of her (body) if he is looking at her for the purpose of marrying her.” [Ahmad] This is what our righteous predecessors were upon.
The method that was mentioned in the question is not permissible as it includes some religious prohibitions. For instance, dissolute people could take this as a means to look at women not for the purpose of getting married to them, but rather just to look at them and talk to them. This could also be a cause for suspicions among Muslims. In addition, a person who wants to propose marriage to a woman is only allowed to look at the woman he wants to marry. In the situation mentioned, he is looking at several women to whom he will not marry. So one has to be cautious about this. Yet, the best guidance remains that of the Prophet and his companions .
Finally, it should be noted that a woman is like a man, she is permitted to ask for marriage and express her will about it. So, it is permissible for her to propose herself to men to marry her as one woman proposed herself to the Prophet in which case, she has to observe Hijab and good moral conduct and this should be in a manner that does not lead to affliction or suspicion.
And Allaah knows best.