Your questions are very nice. Yes, the Supersoul and soul both are unchanged. The difference is that in material contact, the soul appears to be changed. But the Supersoul is not affected by material contamination, therefore there is no sign of change. The change of soul is like that water becomes ice in contact with refrigerator. And as soon as there is temperature the ice again becomes water. Similarly the changing nature of the soul is just like change of water to ice. The tendency of ice is to melt and become water again. So due to contamination of matter, the soul by illusion identifies with material existence. But the tendency is to melt again to Krishna Consciousness. So when there is sufficient temperature in contact with bona fide Spiritual Master and devotees, the soul again becomes Krishna Conscious, like the water.
If someone is fortunate enough to find out a bona fide Spiritual Master, his life is successful. And to be fortunate, there must be sincerity, and Krishna will lead him to a bona fide Spiritual Master.
purusa means God or Krishna. Atma, there is Paramatma and jivatma. Both are atma because they are spiritual, but the living entities are called jivatma. Jivatma means the small particle of atma which has tendency to fall down in the material atmosphere. He is called jivatma. And Atma or Supersoul, Who never falls in material contamination, is called Paramatma or Supersoul. And because He does not fall under material illusion, His another Name is Acyuta—Acyuta means never fallen.