broken part to window that attaches to the metal bracket in pic down inside the window
Thanks for posting! Your balance channel has a grove at the bottom of it so you'll need the 15-236 1-1/4" T-Lock Spring Shoe. Although, if all of these are breaking in the same manner, it may be a good idea to check if the balances might need to be replaced.
These shoes install to the bottom of the balance using a rivet. If this is missing from your balance, then you'll absolutely need to replace the entire assembly. There are also a number of factors that could indicate your balances would need to be replaced but you would ultimately need to examine the hardware to confirm. For example, is there any noticeable damage to the other parts of the balance? Does the window seem heavier/harder to open?
Given that the shoes have started becoming detached from the balances in the same manner and at the same time, it is very likely they do need to be replaced. Especially since you've confirmed the balances have failed in the channel.
In that case, you won't need the 15-236 since you would be replacing the entire assembly.