"Pagka-/Pagkaka-" affix has several uses: A certain fact, state or condition. (eg. pagka(ka)matay = being dead). Sobra niyang ikinalungkot ang pagkamatay ng kanyang aso. = Transliteration: He is so upset about his dog being dead. Translation: He is so upset about the death of his dog. Manner by which something was done. (eg. pagka(ka)patay = manner or way somebody was killed) Ang pagkapatay sa kanya ay masyadong brutal. = The way he was murdered was too brutal. Corresponds to time clause after/right after/as soon as. (eg. pagkamatay = right after somebody's death) Nakuha niya ang mana pagkamatay ng kanyang lolo. = He got his inheritance after his grandfather's death. Your sentence falls under the first use which denotes state or condition and not under the second one which is about the manner in which the action was done. "Ang batà ay pinapayat ng isang matagal na sakít." is in active voice so it could translated to: The boy was emaciated by a long illness. "Ang batà ay pinapayat ng isang matagal na pagkakasakít." If we were to transliterate it, it'd be The boy/child was emaciated by being in a long state of illness. You see, applying the first use only adds drama. Because in my example above, I could've simply said: "Sobra niyang ikinalungkot ang kamatayan ng kanyang aso." which gives out the same thought that some "he" is just devastated with the loss of his dog. Good luck! ;)

I think, it's the same. There's no difference because pagkakasakit and sakit is the same in the use in that sentence. They are both noun. Yet, if you use 'sakit' in other sentence just like.. 'Ang sakit niya ay lagnat' which means His sickness is fever, it'll be different compared to pagkakasakit which is present verb if you use in other sentence.