Hello,
The current situation is as follows :
Two LAN cards on the system :
1.Connected to the internet
2.Other one creating a LAN and providing internet with conditions imposed by using squid.(IPs are manually assigned and not a VLAN)

Two issues :
1.One cannot ping a public IP from within the LAN (for example :
system ip : 192.168.250.102
can ping another system with ip 192.168.250.106 but cannot ping google.com )
2.Is there a way in squid to control the download limit and provide user authentication (in sense the user has to give in a password to access the net).
Thanks.

Squid is a web proxy; it supports the HTTP, HTTPS and FTP protocols. Ping uses ICMP.

In order to ping a host on the Internet (or use any protocol other than the three supported by squid), you need to configure your gateway to perform IP address translation on outgoing connections, hiding the internal, non-routable addresses behind the public IP of the gateway. You can't do this with squid; you'll have to use iptables/netfilter.

Squid can be set up to require authentication. A Google search will turn up lots of howtos and examples (like this page and this page).

I'm sure it can do download and bandwidth limiting too, although I've never tried that myself.