Is opening forbidden websites in private considered a form of the "fornication of the eyes"? And will the girl be punished if she repents with sincere repentance?

If the questioner looks at forbidden images, this is a form of adultery of the eyes. She must hasten to repent and stop accessing these websites. If she is granted sincere repentance, Allah will accept her repentance and forgive her sin. What helps with steadfastness and maintaining prayer is to feel Allah's watchfulness over her, to be keen on good companionship, to fill her free time with what benefits her, and to avoid being alone with devices that tempt her to access wicked websites.