第一题是因为ill是个形容词而且是个表语形容词.
说它是表语形容词,那它就要和系动词一起使用,系表结构做谓语,这个系动词可以是be,get ,become如果没有系动词,只用ill没法借助动词do完成疑问句.可以改成：
How often do you become ill?
How often do you get ill?
How often are you ill?
第二题是一个固定短语be away from.“从.离开”