Am I sinful for having eaten from ill-gotten gains when I was young and unaware? And if I owe a debt to a female student and do not know her whereabouts, how can I repay this debt?

You must pay the value of the potatoes you ate to the cafeteria owner. If you do not know the exact amount, make an effort to estimate it and ask for his forgiveness. If you fear fitna (strife/temptation), return the money by any means. If it is impossible to deliver his right to him, then give the money in charity with the intention of the reward and recompense going to its owner. The same applies to the riyal you borrowed from your colleague; if you cannot return it to her, then give it in charity on her behalf.