Hello Ricky,
Thank you for your concern, sorry for not responding on time, I just came back from leave. After configuring the NAT and Squid (in transparent mode) as you specified in your tutorial, I configured the workstation to use the linux server DNS and it worked fine. I noticed that the squid cache (/cache) refuse to increase in size after checking for some time. I decided to run /opt/squid/sbin/squid and it gave its process ID.
I removed /etc/rc.d/rc.nat from the /etc/rc.d/rc.local file and restarted the system. After restarting I reconfigured the workstation browser to use 192.168.1.1 and 3128 as its proxy address and also was browsing. So I do not know what to do so that squid can start caching web pages.