Is it permissible for a man to search for other matchmakers, then return to propose to a girl he saw previously and rejected, feeling that he wronged her by rejecting her without delving deeply into seeing her and speaking with her, or could that lead him into the forbidden?

No injustice befalls a girl if a suitor declines her after seeing her, and it is permissible for the man to propose to another. It is permissible for the suitor to repeatedly look at the prospective bride if he needs to, in order to find what would motivate him to marry her, as the Prophet (peace and blessings be upon him) said: "If one of you proposes to a woman, and he is able to see some of what would motivate him to marry her, then let him do so." And his saying to Mughira ibn Shu'ba: "Look at her, for it is more likely to engender affection between you." If the mother was impressed by the girl, it is permissible for the young man to look at her again and seek Allah's guidance (istikharah). If he finds what motivates him to marry her, then let him marry her; otherwise, let him seek another.