By Gram Slattery, Andrea Shalal, Andrew Gray and John IrishWASHINGTON/BRUSSELS/PARIS, April 3 (Reuters) - The NATO alliance has in recent years survived existential challenges - ranging from the war in Ukraine to multiple bouts of pressure and insults from U.S. President Donald Trump, who has questioned its core mission and threatened to seize Greenland.But it is the U.S.-Israeli war with Iran, thousands of miles from Europe, that has nearly broken the 76-year-old bloc and threatens to leave it...