Thanks All,
I finally solved the problem using the clues you provided.
It turns out the YAST configuration utility (and my ignorance) combined to mess up the interface configuration files for the NIC card and the bridge. After manually fixing the config files, the Xen Dom0 is running on a DHCP IP address and the DomU is running on a static IP (on a different subnet) with no issues.
On the Dom0 - when the bridge is properly configured - the ifconfig command will show the DCHP-assigned IP address attached to the br0 bridge, while the NIC card will show no IP address. Manually, once the bridge was created by the Xen install, I could set the network parameters on the bridge by editing /etc/sysconfig/ifcfg-br0. Make sure the NIC card is listed in the PORT= line (this was missing in my config file). In the same folder, the ifcfg- file for the NIC card should NOT assign an IP address. In my case, I deleted the file (ifcfg-enp2s0) and everything worked fine.
I also found out it was important to have the SuSE-firewall2 running. The firewall includes iptables routing instructions that send all incoming packets into the NIC card onto the bridge. Apparently, whether the NIC packets are sent through the iptables/netfilter system on the Dom0 is controlled by some kernel parameters like:
net.bridge.bridge-nf-call-ip6tables
net.bridge.bridge-nf-call-iptables
net.bridge.bridge-nf-call-arptables
Depending on these values, the Dom0 kernel sends NIC packets directly onto the bridge before or after going through iptables. These parameters can theoretically be changed via sysctl and /etc/sysctl.conf, but try as I might I could not get the kernel to reboot with the correct values. There is some chatter on the internet that this might be bug related. In any case, in OpenSuse 13.1, the default values direct packets through iptables. With the firewall on, there appropriate iptables information was there to direct packets onto the bridge. However, if I turned the firewall off, the Dom0 could not longer see the internet.
Once this is done (and the network restarted), my DomU was set up with a static IP using YAST in the usual way. Everything seemed to work.
So in a nutshell, it seems that my YAST configuration had somehow led to the NIC card being stripped from the PORT= entry in the /etc/sysconfig/ifcfg-br0 file in addition to separate IP addresses being assigned to both the bridge and the NIC card. After that, there was no hope…
Useful commands to debug:
ifconfig - to see the interface settings
brctl show - to see which interfaces are attached to the bridge
iptables --list - to see how dom0 kernel is handling interface packets
sysctl -p - to see the settings on kernel parameters
route -n - to see routing information by IP address/network
Useful references:
https://www.suse.com/communities/conversations/basic-iptables-tutorial/
http://www.thegeekstuff.com/2011/01/iptables-fundamentals/
http://www.thegeekstuff.com/2011/06/iptables-rules-examples/
http://www.linuxfoundation.org/collaborate/workgroups/networking/bridge