Is what the questioner is doing—informing a girl of his love for her through a female relative, asking her to wait until he graduates and establishes himself, along with supplicating in prayer and performing Salatul Hajah with the intention of marrying her—considered correct or incorrect?

There is no harm in being attached to a girl, desiring to marry her, and supplicating for that. However, if you are unable to marry, then it is proper to divert your heart from this attachment and occupy yourself with what benefits you in matters of religion and worldly life, especially since you are at a critical age with responsibilities for which you will be questioned on the Day of Judgment. The Messenger of Allah, peace and blessings be upon him, said: "The feet of a servant will not move on the Day of Resurrection from before his Lord until he is asked about five things: about his life and how he spent it; about his youth and how he wore it out; about his wealth, from where he acquired it and on what he spent it; and what he did with what he knew."