Correct! Direct compression (and wound packing) are effective hemorrhage control methods and are the foundation to the Stop-The-Bleed training programs.  

Incorrect. There are no major vessels posterior to the mastoid process.  This region has the sternocleidomastoid muscle and other deep neck muscles and is ineffective for hemorrhage control. 

Correct! The facial artery arises from the external carotid artery and crosses the ramus of the mandible. As the facial artery supplies the angular artery, compression here will reduce flow in the angular artery.

However, since the distal end of the angular artery anastomoses with the deep vessels supplied by the maxillary artery, compression of the facial artery will slow but not stop bleeding.

Incorrect. This would reduce blood flow to both the superficial and deep vascular supplies to that side of the face (as both are feed by the external carotid artery).

However, the common carotid artery compression would also cut off blood flow to the internal carotid artery and reduce cerebral blood flow. The circle of Willis in the brain does provide collateral supply from the other side internal carotid artery (and vertebral arteries), blocking the common carotid would be far ideal.

Incorrect. Directly below the chin has just some muscles of the floor of the mouth. There are no major vessels in this location so compression here would be ineffective.