3.But he left the PDP in a fury after falling out with Obasanjo.

fall out with与某人决裂，争吵

例句：They fall out with each other just before their marriage.

他们就在举行婚礼之前吵了起来。

1.The High Court upheld a ruling at the inquest that the families of the 52 people killed in the 7 July suicide attacks should be allowed to hear evidence given by agents from the domestic spy agency MI5.

这句话的主干是：The High Court upheld a ruling at the inquest。that引导的是ruling的同位语，说明详细内容。be allowed to被允许做某事。

2.The Italian Prime Minister Silvio Berlusconi promised to end the crisis, which has been blamed on a combination of underinvestment, poor management and mafia control of some of the dump sites.

这句话的主干是前半部分，which引导的是定语从句。

3.The Mexican government has advised migrants driving home from the United States for the winter holidays to form convoys for their own protection as they pass through Mexico.

advise sb to do sth建议某人做某事。

advise的用法

1)用作及物动词时，注意后接动名词 (不能直接跟不定式)或不定式的复合结构：

正：He advised leaving early. 他建议早点出发。

正：He advised us to leave early. 他建议我们早点出发。