Balancer?
The part you're showing us is actually called a "pivot bar". It connects to a pivot shoe, which is connected to the balance, and helps with the operation of opening and closing the windows. So, in a sense, you are correct. That said, let's have you take a look at our 26-378 pivot bar. We'd like for you to carefully compare your measurements with ours to see if they are compatible with one another.
I am afraid we do not offer replacement screws. Since we do not know the depth for which these parts are being installed into, we recommend reusing the original screws. If you no longer have the original ones, you can visit your local hardware store where assistance can be provided on a replacement.