What size shoe pivot and balanced
I'm afraid your existing hardware is a little too damaged for me to identify. I also don't know your precise measurements, so I won't be able to give you a second opinion on that front.
What I can tell you is that this appears to be a pretty typical tilt window. There are only two options for the spiral balance: either the Series 900, which has a 3/8" diameter tube, or the Series 600, which has a 9/16" diameter tube. Yours looks like it might be the 9/16" variety but you will need to make the final judgment for that.
As for the shoe, you will need to remove an undamaged version from the window to get accurate measurements. The most important dimensions are width and thickness. Height doesn't matter so much so you can ignore that. You can see our full selection here.