Does the Hadith, "Whoever fasts Ramadan out of faith and hope for reward, his past sins will be forgiven," include those who broke their fast for some days of Ramadan due to an excuse, or is it exclusive to those who fasted the entire Ramadan?

The apparent (and Allah knows best) is that a sick person who intended to fast but did not fast due to the excuse of illness will receive the reward, as explained by Al-Kirmani in "Fayd al-Qadeer," reasoning by analogy with the prayer of one who sits due to an excuse.