Is it permissible to marry a young man who works as a cook in a restaurant that serves alcohol on another floor, given that he works on the floor that only serves halal food, and is his work unlawful?

If the young man does not work in selling alcohol or assisting in it, then his work is permissible, according to the preponderant opinion. This is because the commingling of the shop's money does not make dealing with it unlawful, unless he knows that his salary comes from unlawful sources. The Prophet, peace and blessings be upon him, and his companions dealt with Jews despite their engagement in usury and consumption of unlawful wealth. He would accept their invitations, eat their food, and pawn his shield with them.