Is intermixing forbidden in all circumstances, such as in public transportation and airplanes, and is one sinful for sitting next to a woman due to the unavailability of another seat, and what is the ruling on intermixing in markets, and what is the ruling on a woman sitting with her husband while he is sitting with his friend?

Forbidden intermingling (ikhtilat) is that which leads to temptation (fitna) and does not guarantee freedom from suspicion. However, for someone compelled to be in a mixed environment, such as an airplane passenger, they must fear Allah, avoid temptation, and not expose themselves to it. It is not permissible for them to touch a non-mahram woman. If a woman is with her husband, dressed in Islamic attire, and does not speak provocatively to non-mahram men, then this is not considered forbidden intermingling.