If you are moving from not using a proxy to using squid there are some functions that your browser will no longer be completing.
Using the "Name Error" you mention as an example...
Without a proxy, the browser will attempt a DNS name lookup from the local resolver and it will fail which results in a local application error.
When you use a proxy your local browser does not do DNS name lookup. It opens a connection to the proxy and sends it the URL, so the proxy does the lookup, has the resolver error then sends a http response back to the browser as that is the only interface between the two.
You can always copy and modify the squid error pages to match your browser (somewhere like
/usr/share/squid-langpack/templates and then set
error_directory). Or further customise your browser to provide your custom error messages for particular http error responses from squid. You may need to create simpler tags in the squid error pages that your browser can match easily.