Why should 不 go before 应该？
应该 = should; 不应该 = shouldn't. It could also be "应该不去工作" Should not go...
I think 不应该 would slightly emphasize that the speaker is saying DON'T do this or that while 应该不... just indicates you shouldn't. But really they're pretty much the same.
Funny...I'd say 她生病了，应该不去工作
Yes yes yes... why 不 must goes before 应该???
"go to work" would be better translated as "去上班"
Isn't "go to work" just 上班？Does it even need 去？
yes and no. 去上班 feels to me like go to work on that day, like 我今天去上班 I am going to work today, while 上班 isolated feels to me like a more general statement, like 周末我不上班 I don't work on weekends
Both are right, 上班 alone can have the meaning of "go(ing)" to work
Agree. The hover over tips say '上班'. So we would expect that to be accepted.
Why can't it be 她不应该... -- two sentences, like in English?
I put 她生病了她不应该去工作 and wonder why it is not accepted.
If the sentence is in present tense, why use 了?
生病 acts as a verb here, so instead of "she is getting sick" (她生病）we say "she has gotten sick" (她生病了）。
Is 生 really necessary in this case?
yes, 病 by itself doesnt mean sick as in illness but more so, "sick in the head"
I beg to differ, but 她病了 is perfectly fine. If you want to mean it in a sarcastic way, the most common would be to use 有病