Is Southern a proper adjective

Answer 1

No, it is a common adjective, unless it is part of the name of a particular place. It means 'pertaining to the south', which similarly is not a proper noun unless it forms part of a specific place name.

'I live at the southern edge of the town.'

'He lives in Southern Heights, which is located a few miles to the south of Marbury.'

'She lives on the south side of the river.'

'They travelled to the South Pole.'

Answer 2

No, "Southern" is a proper noun used to describe things related to the south.