What does it take to be forgiven and for a sin to be wiped from a person who commits this act in a time of hopelessness and despair? Is it worth it for this person to pursue a Jewish life or will he/she be eradicated from the next world entirely no matter what?

Shalom, Thank you for your question. One of the major principles of Judaism is the ability to do Tshuvah – repent. This is in the hands of all sinners – no matter what the sin. It involves a process of remorse (which it sounds as though you already have gone through), confessing the sin to Hashem in prayer (privately), and committing to never returning to the sin the future. We are taught that this process of tshuvah is very strong, and can rebuild the souls purity and connection to Hashem – sometimes in ways that are even stronger than what existed before. As to “wiping out” the sin – this is in the hands of Hashem. You should focus on the process of tshuvah, and leave all else in His hands. One should certainly pursue a Jewish life - it is the voice of despair that lies to a person and tells them there is no hope. The opposite is true – a happier and more fulfilled life awaits those who return to Torah and Hashem, both in this world and the next. May you be blessed with all that’s good.