identifying my pivot lock shoe

Hello! Your shoe looks very much like our 15-192 Certainteed brand pivot shoe at first glance. Check it out and let me know what you think.

That cutout is definitely where you want to take the shoe out, yes. The part you see there is part of the coil balance assembly, for which the pivot shoe itself is only one of many components. You will need to take the whole assembly out of the window in order to replace the shoe.

I'll also share a few videos that you may find helpful. These explain to you what kind of balance system you have and how it all fits together, as well as how to remove a similarly-designed balance from the track.

They definitely should be connected, otherwise your windows wouldn't stay up when you open them. If for whatever reason your springs are not connected to the shoes then something has gone very wrong. That is how they're meant to function.