Hi,
2. Should I exchange only the fan or fan and cooler?
You shouldn't exchange any of them, if they still work.
When a fan gets loud and the system's case gets hot, there is often dust (or something other) blocking the airflow. Such notebook fans s u c k cold air from the bottom side and blow it outside in a 90° angle through the cooler fins, where the cold air takes the heat from cpu and other hot system components.
Can you feel a hot airflow coming out of the case at the fan position? If not, that is often a sign of a blocked airflow somewhere.
These pictures show an example of a dusty notebook cooler, that had to be cleaned 
:
You should check the cooler fins (outtake) and the grid (intake) at the bottom under the fan. Try to clean these positions carefully.
Don't remove the cooler, if you have no experience with cooler installations. I don't know your cooler, but sometimes (often) you have to clean the cooler surface and the heat spreader of CPU and other components, replace thermal grease and so on. If you do something wrong here, your system may take serious damage.
Joutungwu
PS: No reasen to hide (******) s u c k here, Sony. It just means s u c k. 