【1】Jeffery was one the dozens of signatories of the ‘Never Trump’ letters by leading Republic national security officials.

修改：

Jeffery was one the dozens of signatories of the ‘Never Trump’ letters by leading Republican national security officials.

解释：Republic是共和国，而Republican才是共和党

【2】Followed that, it was discovered that when she first registered in Britain in 1995 Alemi had conned medical bodies into believing she had a qualification from the university of Auckland in New Zealand.

修改：

Following that, it was discovered that when she first registered in Britain in 1995 Alemi had conned medical bodies into believing she had a qualification from the university of Auckland in New Zealand.

解释：A、B两件事，A followed B，表示A在B后面，转为分句表达时，就成了Following B, A…，换个句型你就明白了。I opened the door，转为分句表达，Opening the door, I saw a bird flying over.

【3】A flash flood watch is effect Wednesday through Friday for the Camp Fire area, where 3 to 6 inches of rain are expected

修改：

A flash flood watch is in effect Wednesday through Friday for the Camp Fire area, where 3 to 6 inches of rain are expected.

解释：原句的effect是名词在is后面没有逻辑意义。改为in effect表示生效，有效，或在进行中的类似含义。

Are expected还是is expected有争议。