Fragen über die Beispielsätze mit, und die Definition und Benutzung von "Cda"

A: × I am requesting to take CDA course and COP course for the fall 2021 semester.
✓ I am applying to take the CDA course and the COP course for the fall 2021 semester.

× However, if I am not able to take COP class for this fall, I should take 2 general elective courses which I already fulfilled the required 12 credits.
✓ However, if I am not able to take the COP class this fall, I should take 2 general elective courses, for which I already fulfilled the required 12 credits.

× Furthermore, my expected graduation year will be postponed.
✓ Furthermore, my expected graduation date will be postponed.

To be clear, what you wrote was perfectly understandable. In the first sentence, "applying" would normally be the correct term. However, if you normally would not be allowed to take those courses and want an exception, you could instead say, "I am requesting special permission to take ..." instead.