From what I remember of Red Hat:
1/ You need to create this script and chmod 777 it: /etc/sysconfig/network-scripts/ifcfg-eth0
# start eth0 on boot
BOOTPROTO=dhcp #get ip address from your isp dhcp server
I think you may also need to load your eth0 module by inserting the following line in /etc/modules.conf
2/ With respect to sharing your ADSL connection, I understand your LAN as follows:
ADSL modem --> (eth0) Linux Box (eth1) --> Windows Box
You stated that your Linux box can ping to your Windows box, so obviously you have configured your eth1 properly.
To share your ADSL connection, your Linux box will act as a router. Use iptables to do NAT ip masquerading. Create (and chmod 777) /etc/init.d/iptables:
# load iptables modules
# enable ip forwarding
/bin/echo 1 > /proc/sys/net/ipv4/ip_forward
# flush tables
# enable masquerading to allow LAN internet access
$IPTABLES -t nat -A POSTROUTING -o eth0 -j MASQUERADE
# forward LAN traffic from eth1 to eth0
$IPTABLES -A FORWARD -i eth1 -o eth0 -m state --state NEW,ESTABLISHED -j ACCEPT
# block out internet intrusion on eth0
$IPTABLES -A INPUT -i eth0 -m state --state NEW,INVALID -j DROP
$IPTABLES -A FORWARD -i eth0 -m state --state NEW,INVALID -j DROP
The above is a simple iptables script that will allow internet sharing on a home LAN. If you search this site for "iptables" and/or "firewall" you will find examples of more complex iptables scripts. Also search under user "mychl".
3/ I don't know what you mean by making the devices appear correctly in the GUI. Do you mean having your Linux box appear in Windows' Network Neighbourhood, or displaying your Windows shares on your Linux box? If so, then you need to search this site for "samba" and "linneighbourhood". I don't network with any Windows machines, so I can't help you here.