If you use the old Cold War definition, yes. Otherwise
However, as the Cold War ended with the dissolution of the Soviet Union in 1991, the definition largely shifted to instead refer to any country that boasts a well-functioning democratic system with little prospects of political risk, in addition to a strong rule of law, a capitalist economy with economic stability, and a high standard of living.
They are involved in their own politics, just like the first world only cares about what happens to the first world.
Israel confirmed first world…?
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If you use the old Cold War definition, yes. Otherwise
No, but they are directly tied to the US.