Is the method mentioned for finding a wife correct, and is one obligated to accept the girl simply upon seeing her, or does one have the right to refuse if she does not appeal to him?

The method you mentioned for seeking a wife is permissible and one of the correct approaches, as women know other women best. Al-Bayhaqi and Al-Hakim narrated that the Prophet (peace be upon him) sent a woman to look at another woman whom he intended to marry. It is permissible for the suitor to look at the woman he intends to propose to if he has decided to propose to her, as stated in several hadiths. The most important quality to seek in a woman is her religious devotion and character, as the Prophet (peace be upon him) said: "So win the one who is religious, and you will be successful." If the suitor finds nothing that encourages him to marry her, there is no blame upon him for leaving her. However, if she possesses religious devotion and good character, it is more appropriate to marry her, for Allah Almighty says: "And perhaps you dislike a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah Knows, while you know not."