LCD - a good question and one which the fare-paying public should be aware of. The limits on FDP and duty have been laid down by authorities and are judged to be safe. I don't know the answer to your question "If a pilot is considered "seriously tired" on approach to landing how does this affect them?" It is quite subjective and generally it is judged that the 'adrenalin rush' of an emergency or the coming landing will overcome tiredness.
I would say, however, that it would be a strange event if several crew all felt they were 'fatigued' at the same time. Tired yes, and 'seriously tired' (define?) possibly. Any crew member who suspects they may be suffering from fatigue must not fly and should report sick - it is the law. If they are so tired that they consider their ability to operate is seriously impaired they should also decline duty - it is common-sense. There is nothing in the ANO that says you cannot operate if you are tired but you must be FIT to operate.
Refusal to operate into discretion is the right of the Captain and the Captain alone. Individual crew members can declare themselves unfit to extend their duty, but I'm sure any company might wish to study pre-flight rest activities and life-style etc in that event, and that may not be a good thing!
I don't know about "fatigue had to be declared within 2 hours and after a rest period to crewing" - sounds like a company edict? I do know that fatigue should be declared to a doctor as soon as it is suspected. The symptoms of fatigue are quite different to those of tiredness. I suspect that if a 'normal' airline roster (as is!) is causing fatigue to a crew member they may be advised to look at a change of occupation.
It sounds as if the Captain may well have been unfit to operate at all and should, in accordance with the ANO, have removed himself from duty. The judgement on discretion needs to be made at the time it is required. If that is before departure, I know that declaring oneself 'unfit' to operate into discretion before it happens is fraught with career-threatening danger! Having been in the 'tired' zone quite a few times myself there are things like controlled in-flight rest, high-speed cruise, no turn-round cleaning etc that can be used to help, and I have on occasion advised ops that my discretionary extension might not be relied on, but I have never declared it to be 'impossible' before departure - as long as it is within the legal limits, of course.
Being "maxed out on my roster" is subjective - it depends on your personal fitness and how you plan your life. It is becoming very common now to work crews to the absolute limit of duty and rostering, despite the 'guidance' given by the authorities on this. If the company is constantly 'abusing' the intent of the scheme, you may wish to consider copying your roster to the authority (preferably via your union, if you have one!). Folk need to know that being airline crew will probably not be a glamorous bed of roses.