Thanks for posting! Your spiral balances appear to be non-tilt window spiral balances. Can you confirm this information? To identify the compatible hardware, I would also need to see those parts removed from the sash, if possible. If you cannot confirm them from this particular window, you may need to double check a similar window in the home.
Also, if you are unsure about the sash weight, it would be best to double check the actual weight of the sash. Especially since the sole purpose of the balances is to support the weight of the sash.
Once I have a better idea of the type of balances you need, we'll be able to provide better guidance on how to remove and install them.
Please let me know if you have any questions in the meantime.
Your balance diameter appears to be 5/8" and the length looks like it could be 35". So, I believe you'll need the S500-35 Spiral Balance. Since the sash weighs just below 30lbs, you'll need to select the red tip option.
It does not appear that we have an exact replacement match for the mounting bracket but the view of it is obstructed in the photo. From what I can see, it looks similar to the 17-011 Side Mount Bracket, N62. Take a look over the dimensions to confirm if this is the right fit.