Is it valid for a pilgrim performing Tamattu' Hajj to fast on the days of Tarwiyah, Arafah, and the second day of Eid, then from the sixteenth of Dhul-Hijjah until the twenty-second of it, and would he be sinful for fasting on the Day of Arafah?

Whoever performs Umrah (definition) with the intention of performing Hajj (Umrat al-Mutamatti) is required to offer a sacrifice (hady). If they cannot find one, they must fast for ten days: three during Hajj and seven upon returning to their family. Fasting during the Days of Tashreeq is permissible for those who cannot find a hady. It is preferable to fast the three days before the Day of Arafah so that one can break their fast on that day to gain strength for supplication. The seven days of fasting should be observed upon returning to one's family, though it is permissible to fast them in Mecca or on the way.