Is it Islamically permissible for a person to ask their Lord to show them in a dream the image of the girl who will become their wife, and how can one be sure that what they see in the dream is from Allah and not just confused dreams?

The wise Shari'ah encourages supplication. Allah Almighty says: "And your Lord says, 'Call upon Me; I will respond to you,'" and He also says: "And when My servants ask you concerning Me, then indeed I am near. I respond to the invocation of the supplicant when he invokes Me." It is permissible for a person to supplicate for anything concerning the affairs of this world and the Hereafter, as long as there is no sin in it. The proof for this is the Qudsi Hadith: "Let one of you ask his Lord for his needs, even for salt, and even for the shoelace of his sandal if it breaks." And in Sahih Muslim, a Hadith narrated by Ibn Mas'ud states that the Prophet (peace be upon him) said: "Then let him choose whatever he wishes to ask for." Therefore, there is no harm in supplicating that Allah show you in a dream the image of the girl who will become your wife. However, a wise person supplicates for that which brings benefit or wards off harm, and there is nothing of that in such a supplication. Whatever a person experiences as a vision in their dream is all by Allah's decree and destiny. What is good is called a vision (ru'ya) and is attributed to Allah, and what is mixed or contains evil is called a dream (hulm) or confused dreams (adghath ahlam) and is attributed to Satan. It is not possible to definitively confirm the existence and realization of what was seen in a dream, except for visions related to the Prophet (peace be upon him), provided that his descriptions (peace be upon him) perfectly match what was seen; for Satan cannot impersonate him. Nevertheless, no rulings can be based on such a vision.