If the needle of a compass is a small bar magnet, then does it mean that the south pole of the needle points toward the north of the earth, while the north pole of the magnet points towards the south?

 

If so, then should we consider this property applicable when we talk about the way a needle reacts due to magnetic fields?

A magnetic needle or a bar magnet have poles, North and South. 

Now, these poles are actually  defined as "North seeking pole" and "South seeking pole".

Since we know that, opposite poles attract each other, so the South pole of needle/magnet should get attracted towards the magnetic North pole of Earth.

Similarly North pole of needle/magnet should get attracted towards the magnetic South pole of the Earth.

 

Hence, you are right in saying that South Pole of the needle points towards the North of Earth. And this pole is named as "North Seeking Pole" or "North Pole" as a convention.