Can one leave his computer on all shabbat linked to an internet news site in order get the latest updates re:the events in the North&South? The screen refreshes automatically and there is no sound.

Two conditions. The web site is not Jewish or Israeli (so that you do not gain benefit from the Chilul Shabbat of a Jew) and the computer buttons are covered, or you put on a sign that says Shabbos so you will not come to touch any buttons. In respect to Israeli news, it may be difficult to guarantee that the camera crew, etc, don't have Jews on board. If you are reasonably certain, then you can watch, but I'm not sure if you can ascertain this. If one is truly concerned about events (thankfully the war is over) getting an update may contribute to peace of mind on the Shabbat. I think, however, that the true Shabbat menucha should come from caring about the situation but allowing Shabbat to go by without involvement in the ongoing news, in order to look at things freshly after Shabbat.