Is paying the bill for alcoholic drinks on behalf of a foreign professor considered a sin, and what are the implications of that?

If what you paid was to settle a debt firmly owed by the professor, then there is no blame upon you, regardless of whether what was carried was permissible or impermissible. However, if you paid the price before it became a debt, then this is forbidden due to cooperation in sin and aggression, and you must repent. You have no legal right to demand the amount paid back from the supervisors unless they instructed you to pay. It is also not permissible for you to accompany the professor to the airport, especially if this leads to forbidden seclusion (khalwa).