几个在阅读中搞不懂的句子，请教各位

OG10CR-102. Very few patients have allergic migraine reactions as children live migraine-free adult lives once they have eliminated from their diets foods to which they have been demonstrated to be allergic.
                    

as children live migraine-free adult lives中children和前面的 few patients  有关系么？后面的once they 中的they又指代哪个？

OG10CR-61. The recent decline in the value of the dollar was triggered by a prediction of slower economic growth in the coming year. But that prediction would not have adversely affected the dollar had it not been for the government’s huge budget deficit, which must therefore be decreased to prevent future currency declines.

句中had it not been for the government’s huge budget deficit,  是不是省略if的倒装：if  it had not been for the government’s huge budget deficit,