Is money earned from unlawful work, such as trading during prayer times, or teaching permissible subjects to immodestly dressed women, or transporting a woman alone, considered unlawful money?

Everything that is inherently forbidden makes the work involved in it and its outcome forbidden. However, for something that is forbidden due to an external factor and not inherently, the work itself is forbidden, but its outcome is not forbidden according to the majority of scholars. They say that the worker disobeyed Allah, but the act itself is valid.

"And that which is forbidden is invalid" is a comprehensive rule applicable to both acts of worship and transactions. Anything forbidden in the Qur'an or Sunnah is considered invalid.

The examples mentioned in the question are not inherently forbidden, and therefore their outcomes are not unlawful. However, the doer is sinful. This is why scholars said, "He disobeyed and it was valid," arguing that an action has two distinct aspects, and the prohibition is due to an external matter, not inherent to the action itself.

Among the proofs for this is the consensus of the Ummah on the validity of the fast of one who fasted on a day when he feared perishing, and the validity of the prayer of one who prayed in a land from which migration is obligatory.

Based on this, selling by someone who is obliged to attend congregational prayer at the time of the obligatory prayer is valid, unless it is Friday prayer, in which case the sale is invalid due to the prohibition.

Similarly, one who teaches immodestly dressed women or transports them has not committed what is inherently forbidden, but rather cooperated in sin and aggression. Thus, he disobeyed, and his action is valid due to the separation of the two aspects.