Is it permissible to exchange a first-class travel ticket for an economy class ticket and take the financial difference, and is it permissible to take what remains of travel expenses, accommodation allowance, and food allowance, and what is the ruling on swearing by the heart without uttering it with the tongue?

The basic principle is that an employee may dispose of what is granted to him as valid ownership in any permissible way, unless it conflicts with the company's regulations and conditions, or if he knows that the company does not allow it. Therefore, disposing of a discounted travel ticket—by selling it, exchanging it, or gifting it—is permissible unless it conflicts with the conditions of the granting and transporting company. As for an oath made within oneself without utterance, it has no effect, as the majority of jurists stipulate verbalization for an oath to be binding.