According to the exhaust pipe manufacturers instructions, at least one inch must be maintained between the exhaust pipe and any combustible material. I recommend removing the wall stud and bypassing the ceiling joist in order to provide adequate clearance for the exhaust pipe. This condition is a safety concern. The mortar on top of the chimney is cracked and deteriorating. The mortar chimney cap is the first line of defense against rainwater penetrating the bricks and mortar in the chimney.
Water can deteriorate the mortar and cause structural damage to the chimney.
This condition has caused the door casing to move at the threshold when opening and closing. This condition has also caused the door not to seal properly against the weather-stripping at the top when closed. Securing of the threshold to the slab is recommended. The fan blade, which is mounted directly on the motor shaft, will not turn. The plywood roof sheathing is damaged on the left side of the chimney.