1. Your sprite collection? Doesn't matter - since you're calling make pixel perfect on it, it doesn't matter what the size is set. The sprite going big/small is expected - the further away it is from the camera the bigger it must be to be pixel perfect, no?
2. You should rotate it. Again - this isn't necessary if you do option #2 from before, as you'll be drawing the sprite into a different camera.
3. You requested a way of making the sprite pixel perfect - it would be the same size everywhere on screen if it was pixel perfect, wouldn't it? i.e. 1 pixel in texture = 1 pixel on screen. Thats why it gets bigger and smaller with the perspective camera.