She has fallen ill for a week

不对，fall ill是短暂性动词词组
应该说She has been ill for a week或者She fell ill a week ago

she has been ill for a week
fallen is an action which cannot last.

不对，fall是瞬间动词
应该改成 she has been ill for a week

不对， fallen 是短暂性动词不能接表时间段的状语（for a week），再从句意上分析，说话人想说他已经生病一个周了！
是说那个人处在生病的状态是一周了，而fallen是表示生病，“生”这个动作，就是从健康到病的变化过程，这个过程不能是一周吧！
this is my answer! i hope it can do you a little help !