Observing compensatory Sawm for six days during Shawwal is not counted as the six-day supererogatory Sawm of Shawwal. This is because one should not begin observing the six-day supererogatory Sawm of Shawwal unless one has already made up for the days they missed during Ramadan. This is based on the following Hadith in which the Prophet (peace be upon him) said:
Anyone who observes Sawm of Ramadan and then follows it with six days (of Sawm) in Shawwal, it would be as if they had fasted permanently.
Accordingly, it is obligatory for a person who still has some missed days of Sawm from Ramadan to start compensatory Sawm before observing the six-day supererogatory Sawm of Shawwal.It is permissible to combine the intention for performing `Umrah and Hajj at the same time, since the rites of `Umrah are part of Hajj which is more inclusive than `Umrah. The Prophet (peace be upon him) said:
The (rites of) `Umrah will remain part of Hajj (Part No. 9; Page No. 306) until the day of Resurrection.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.