It is to much reading :). However, I believe that I should not configure squid right now.
This problem actually started when I installed new ADSL modem (Sitecom WL-154).
I still have my old modem (SpeedTouch 570), and when I install it back, the squid starts normally.
The difference is that somehow my Linux hostname is not visible for the LAN.
The old modem has DNS server, which contains the hostname table.
The new modem has no DNS sever. Still, in the modem “DHCP IP Pool Summary” tab, it shows the hostnames of my Windows machines. For Linux machines it only lists IP and MAC addresses. Somehow Windows hostnames are visible for the LAN.
The question is, why Linux does not broadcast its hostname?
When I ping its hostname in Linux, I see only loopback adapter 127.0.0.2.