Both of these claims are staples of Holocaust denial and not surprisingly, both are complete nonsense.

The "Jewish Declaration of War" typically deals with the report that the Zionist leader Chaim Weizmann announced his support for the Anglo-French alliance in September 1939. While Weizmann was certainly an important Jewish figure, he did not speak for all Jews and was not the leader of a Jewish state, since such a thing did not formally exist. Moreover, it was not a declaration of war, but rather it was a declaration of support for the British and French. Within the highly contested political landscape of Mandate Palestine, such gestures had tactical importance for Zionists. Acting like he was the Jewish force in Palestine who supported Paris and London was a way to curry favor with the two Mandate powers within the Middle East. Furthermore, the general world opinion that Germany was an aggressor, rogue state in 1939. The Munich Agreement was in tatters with the German occupation of the rump Czechoslovakia and however reluctant the Allies were to go to war over Poland, a good chunk of public opinion in the UK and France accepted that it was now necessary. Most nonstate actors in Europe and the Middle East during early days of the war were condemnatory of Germany's actions and it was only the surprise Molotov-Ribbentrop Pact that altered the equation somewhat.

As far as boycotts, the two linked headlines are accurate. There were many announced boycotts of Germany and German goods after Hitler's seizure of power in 1933. Not surprisingly, a number of Jewish groups initiated these boycotts, but there were other groups that led these movements. The Third Reich's open antisemitism and violence meted out to Jews obviously stimulated a reaction among the Jewish diaspora. None of these boycotts were the result of state policy, nor did they impact American trade policy vis-a-vis Germany. American firms still did business with Germany, albeit under terms set by Berlin. American-German trade did decline considerably over the 1930s, but private boycotts of Germany were only one part of the picture. Berlin's autarkic drives, shell-games with foreign currency, moves to bilateral trades and protectionism, and German rejigging the German economy for rearmament arguably played a far bigger role in the decline of this transatlantic trade relationship. Since these boycotts were not part of state policy, they were not a hostile act on the part of the United States or other countries.

While such newspaper headlines did report on the news of the day, relying upon them alone is highly misleading. Much as clickbait today relies upon catchy and extreme headlines, so to did the media landscape of the 1930s. Some Jews in the US and other countries did call for international Jewish solidarity in the face of Nazi antisemitism and dictatorship, but this does not mean "Jews of all the world unite in action." That such newspaper headlines feature in Denialist tripe is not surprising as one of the staples of Denialism is that even though the Holocaust did not happen, Germany was justified in rounding up Jews into camps because of such declarations of war and hostility. As with much of Holocaust denial, such a conclusion relies upon simplistic thinking and extrapolating questionable conclusions based on very narrow evidence.