Will a broken system proxy expose the local network
No. If the local proxy fails, the store window still uses the node. It does not fall back to this computer's broadband.
No.
System proxy is only the local proxy of the proxy chain. It helps this computer reach the node. Sites always see the store's node IP, not this computer's broadband. How traffic flows is in How the proxy chain works.
If the third-party app is off, system proxy cannot connect, or the local proxy drops, the store window does not start using this computer's network. Pages either still leave through the node, or they fail to load. This computer's real IP does not become the address the site sees.
The account, password, orders, and seller pages are encrypted before they leave this computer. Even if the local proxy is still forwarding traffic, it only sees that encrypted data. It cannot read it, so the local-proxy network does not leak store contents.