According to the 'official instructions', you are supposed to change the 3 parts (sponge, carbon, BioMax) on a rotating schedule.
If I remember right, you change the carbon every month, the sponge every 2 months, and the BioMax every 3 or 4 months.
Supposedly it's important to change the BioMax every so often, but I don't really know why.
I would say that they need to be changed every so often, but maybe not every 2-3 months as Hagan recommends. Perhaps every 5-6 months or so. And you should just look at the parts, if they look highly clogged and a good rinsing doesn't clean it anymore, probably time to change it.
Regardless of how often you change your filter parts, you should always do it alternating so that you preserve as much of the colonies as possible, thus not crashing your cycle.
Carbon does serve a different purpose, but it isn't always necessary, or even desired.
If you have live plants and add fertilizers like Seachem's Flourish you shouldn't use carbon as it will adsorb/absorb many of the minerals, depriving the plants of them.
If you are using meds you should not use carbon either as it will usually remove the meds from the water. Carbon can be used to remove the meds when you no longer need it.
If you have a need to run some carbon for a short time, say a few days or a week to help polish the water, you can easily buy some, either bulk and a bag or the Hagan pouches, and set it right on top of the filter stack. It may not be quite as effective since all the water isn't forced through it, but if you place it 'blocking' the spillway it should still do a fine job.
You need to rinse carbon before using to remove the dust, but you should use
RO/DI water, or at least a good quality bottled water, or sink/pitcher filtered water. Tap water (treated) will have various minerals in it and the carbon will absorb/adsorb some of it, though probably not too much, but that's the recommendations I've seen to get the best life/performance from carbon.
A lot of people don't use carbon. They cut the filter cartridge open and remove it; or not install it in the stack.
I don't use carbon in my AquaClear since I use Flourish. I have the original carbon bag so I can use it if I need to.