1)It should be noted that the sacrifice that becomes obligatory after performing “hajj al Qiran” or “hajj al Tamattu’” is known as “Dam e Shukar” (The sacrifice of Gratitude). This form of sacrifice does not become obligatory on a pilgrim performing “Hajj al Ifrad”.
Therefore, it is wajib for pilgrims performing “hajj al Qiran” or “hajj al Tamattu’” to offer Dam e Shukar before shaving their heads on the 10th, 11th or 12th of Dhul Hijjah.
On the other hand, the sacrifice that becomes obligatory on a Sahib e Nisab (a person who possesses the minimum amount of wealth) person during the 10th, 11th or 12th Dhul Hijjah is different. This form of sacrifice is obligatory only for individuals who are “Muqeem” (residents), not for those who are travelling. Thus, if a pilgrim stays in Mecca, Mina, and Muzdalifah for 15 days or more, they will be considered as a Muqeem (since some Muftis believe that Mecca, Mina and Muzdalifah are to be considered one single area because their boundaries have been joined with Mecca) and therefore must perform qurbani (as they are Sahib e Nisab). The pilgrim may choose to offer this obligatory sacrifice in Mina, Mecca or anywhere else in the world, although it would be preferable to offer the sacrifice in Mina as this would bring more reward.
To summarise, for pilgrims performing Hajj al-Qiran or Hajj al-Tamattu', two sacrifices are wajib if they are Muqeem and Sahib e Nisab. These sacrifices include the Dam e Shukar and the obligatory Qurbani.
In contrast, for pilgrims who are either travelers, do not possess the minimum wealth, or are performing Hajj al-Ifrad only one sacrifice is wajib, which is the qurbani that is obligatory for them because they are sahib e nisab.
2)For pilgrims performing Hajj or Umrah, both halaq (shaving the head with a razor) and qasar (shortening the hair if its length is longer than the length of a fingertip) are permissible for exiting the state of ihram. However, halaq is preferable. Moreover, if the hair is shorter than a fingertip, then halaq is wajib.