Does the repentance of a young man who committed fornication with a virgin girl, and who regrets his action, get accepted, and will he be forgiven for that, and is it permissible for him to marry her despite his feeling of unease after performing Istikhara?

What happened to you is an enticement from Satan and a following of the self that incites to evil. You must make a sincere repentance, abandon the sin, regret it, and resolve not to return to it, and cover yourself with Allah's covering.

As for marrying the girl, there is no objection to it if her repentance is sincere and her conduct becomes good. This is better for her covering and assisting her. The reluctance from istikharah (guidance prayer) might be due to your future apprehension or your unwillingness to marry an adulteress, which is a natural feeling. Seek Allah's guidance through istikharah and proceed with your matter. If it is good, Allah will destine it for you, and if it is evil, He will avert it from you.