Question

after that, he knew he could any emergency by doing what he could to the best of his ability

get through也有战胜，克服的意思，是不是可以与get over互换

Answer 1

有些相近，但有不同，仔细体会下面的注释，事实上是不能替代的。
get over
To prevail against; overcome.胜过；超越
To recover from:痊愈：
finally got over the divorce.最终从离婚的创伤中恢复了

get through
To arrive at the end of; finish or complete.结束：到达终点；结束或完成
To succeed in making contact; reach.到达：成功地和…联络；到达

Answer 2

不能互换，
get through
到达, 做完, 通过, 度过, 打通比较实际的问题

get over
爬过, 克服, 熬过, 恢复, 原谅心理上的问题

Answer 3

应该是come over