Can anyone explain why fero, ferre, tuli, latum is classed as an irregular verb whilst all of its derivatives (affero, exfero etc... are third conjugation verbs despite the fact that they appear to conjugate just like ferre....?
They're all third conjugation, and the compounded verbs share the irregularity of the uncompounded one. Whatever book you're looking at, I think it wants you to assume that what fero is the compounded forms will be too.
The present stem of fero is basically a third conjugation verb with some irregular forms. That's the reason for the apparent inconsistency in the classification of fero and its compounds (effero or ecfero, not exfero) in the book you're using.