Are there any free local proxy for Linux which cache data and gzip transmitted packages?
It's been a long time since I last used this tool, but perhaps would do what you want, I dont' know... 
_______________Thanks
One more question,
can I use squid for such purposes?
You can use Squid as your proxy-cachw for sure. What I'm not sure about is if it compresses the data (though I suppose It can). So, as far as I know, the answer is half-yes 
Regards.
___________thanks