Does the discretionary punishment for a young man and a young woman intermingling in a public place vary from one judge to another? And can it include imprisonment, especially since the young man is a university student on the verge of graduation and his specialization is "very sensitive"?

In this type of case, there is no specific prescribed punishment (حكم شرعي). Rather, the discretionary punishment (تعزير) is left to the judge's discretion. This may be by word, glance, beating, or even no discretionary punishment at all if the judge deems it a slip from someone with no prior offenses. Intercession is permissible in such cases as long as they have not reached the level of a divine prescribed punishment (حد من حدود الله). The Prophet, peace and blessings be upon him, said: "Intercede, and you will be rewarded," and "Forgive the slips of people of good standing, except in cases of prescribed punishments (hudud)." So, if you find good people who intercede for you to drop the case and pardon it, there is no religious impediment.