Windows – Firefox asks for proxy details, but only when accessing facebook

If you want to configure the browsers of multiple machines in a standard way, just about all popular browsers support the proxy auto-config file. This allows you to have an arbitrarily complex set of rules for whether to use a proxy and which one to use, and means you solve the problem for all popular browsers.

An example proxy.pac that could meet your described requirements:

// proxy.pac: Proxy Auto-Configuration file.

function FindProxyForURL( url, host ) {

    var proxy_spec = "proxy.localnet:3128";

    // Default to using no proxy.
    var ProxyConfig = "DIRECT";

    if(
        dnsDomainIs( host, ".foo.example.org" ) ||
        dnsDomainIs( host, ".bar.example.com" ) ||
        dnsDomainIs( host, ".baz.example.net" )
    ) {
        // Requested domain matches, let's use the proxy.
        ProxyConfig = "PROXY " + proxy_spec;
    } // end if

    return ProxyConfig;

} // end FindProxyForURL()

One thing to try is:

Go to Administrative Tools -> Local Security Policy -> Local Policies -> Security Option, and change "Network security: LAN Manager authentication level" to "LM & NTLM - Use NTLMv2 session if negotiated".

More info that I can't verify (not a Squid user) can be found in :
Getting Squid to authenticate with kerberos and Windows 2008/2003/7/XP