I swear there was another question earlier in this lesson where the correct answer started with "Por qué están ustedes" and I got it wrong because I had "Por qué ustedes están".
I prefer to put the verb first in questions, but Duo almost always forms questions by just adding question marks to statements. So I thought I'd try it their way. Didn't work!!
While 'anxious' and 'worried' are similar and sometimes used as synonyms I would argue that they are still different words... just like 'big' and 'huge'. They differ in a matter of degree. They also can carry other slightly different connotations to the meaning. As this is a teaching app, I would again argue that 'anxious' should not be accepted as a translation of 'preocupado'. Just as you would not translate 'odio' (hate) as 'dislike'. The intended meaning of the sentence could be altered by that substitution.
Yes to both I believe.
I would say 'ansioso' is the stronger one of the two. But that opinion is mostly based on my understanding of English rather than Spanish. But I believe the same holds true for the Spanish. You could think of 'ansioso' as 'really worried' but I wouldn't translate it as such. Rather translate it as 'anxious'. At least in teaching apps like this one.
'Preocupado' can translate to 'preoccupied'. The thing to keep in mind here is that the English word 'preoccupied' can also take on a meaning similar to 'worried' but does typically mean something slightly different. I believe the same is true for the Spanish.
It is important to note that you do want to be careful of something called 'false friends'. Those of two words in two different languages that look similar but really mean different things entirely. I don't believe we are dealing with that here though. Here is a link to common false friends if you are interested.
Sorry, that was a little longer than intended.