Did he truly fulfill his obligation, he who left his work without permission, then took leave for the number of hours he spent outside of work, knowing that he was fully present at his work during this leave, and that a day of leave has the same pay as a day of work?

What you did by leaving work during official hours without permission to attend to your personal matters is not permissible. You must consult your employer to find out if they will overlook it, deduct from your salary, or ask you to work at other times. As for working on other days for free without your employer's consent, that is not correct.