If you don't have the special root certificate installed, the browser will refuse to connect because the certificate being presented is invalid (it's the government spying certificate, which you don't trust, not Facebook's certificate, which you do trust).
Your browser will reject the bogus FB certificate. You can tell your browser to connect anyway with the bogus cert, but it will still be MITM'd. There's no way around this (outside of using a VPN or whatever to effectively remove yourself from Kazakhstan).
Going back to normal, i.e the browser saying that the presented certificate is invalid, yes. But you will not be able to browse anything over a HTTPS connection. (Or do other stuff over PKI based TLS, i.e downloading software updates etc.)
Shoot, I hadn't even considered software updates. If this is installed at the system level, they could MITM any software update mechanism that doesn't use cert pinning, couldn't they? Woof.
Is this voluntary? If I bring a device into the country without this certificate (or if the local removes it from their machine) do things go back to normal?