"How can I call these functions"
some_obj.some_func() #<-- a function call
"How can I make them run constantly"
func _process(delta):
some_obj.some_func() #<-- called every frame
func _physics_process(delta):
some_obj.some_func() #<-- called every physics frame
"While taking delta time into account"
Since you're just getting the camera's position or the camera's screen center, you don't need to, the position is what it is. If you were setting the camera's position over time, you would want to consider it.
var new_pos = cam.global_position.linear_interpolate(desired_pos, delta * move_speed)
You can even lerp it along two different values at two different speeds:
cur_offset = cur_offset.linear_interpolate(desired_offset, delta * offset_move_speed)
cur_pos = cur_pos.linear_interpolate(desired_pos, delta * move_speed)
camera.global_position = cur_pos + cur_offset