Is TLV open skies with Airlines or is Norwegian prevented because it is not an EU airline ?
Norway along with Iceland and Liechtenstein are members of the the European Free Trade Association and the European Economic Area. It in turn allows the EFTA-EEA states to participate in the EU's Internal Market without being members of the EU. They adopt almost all EU legislation related to the single market including borders (Norway is in Schengen) except laws on agriculture and fisheries.
So the answer is that Norwegian is not prevented from flying from any EU/EEA airport to TLV.