Is it necessary to see a doctor for a finger dislocation? How is a dislocation defined? It has to be far out of position?

Yes . See a doctor. What might appear to be a simple dislocation might be a complex injury, such as a fracture dislocation. See a doctor for x-ray and examination. A dislocation means the joint is completely out. A patial dislocation is referred to as subluxation.
Not necessarily. ...But is recommended. A dislocation is when the normal alignment and position of the bones in a joint, relative to each other, have been moved. This can, and usually does, damage the ligaments that normally hold the bones together. While one might be able to reduce the dislocation themselves or sometimes this may occur spontaneously, the damage to soft tissue may require further treatment.