Translation:I asked that she did not look in my bag.
While I cannot agree with all of the proposed alternative translations, I believe that unomundo's basic observation is correct, in that Duo's English sentence "I asked that she did not look in my bag" is not grammatically correct. This is a consistent issue with Duo's translations which involve the English mandative subjunctive or present subjunctive.
As andre.v8 correctly points out, and as I'm learning, translating tenses directly between languages is folly. In this case, while the Portuguese sentence uses the imperfeito do subjuntivo tense, it is translated into the English present subjunctive. It is called present because it looks like the English present indicative, and not because the action must necessarily take place in the present time.
I would submit that reasonable translations for the Portuguese sentence are:
I asked that she not look in my bag
I asked her not to look in my bag
I think that the majority of the English sentences in this Subjunctive-Past section sound very awkward and unnatural. I really hope that Brazilians doing the reverse tree or reverse exercises don't get led astray.
Hopefully the Portuguese sentences in this module are relatively natural though, as it has been quite difficult to get through.
No, because the tense in portuguese is in the past, so it can't be how you put it. "Olhasse" is imperfect subjunctive of "olhar", so your sentence would be "Eu pedi para ela não olhar na minha bolsa" (for the first two) OR "Eu perguntei se ela não olhou na minha bolsa". It's hard to translate tenses from portuguese to english and back because english has much less variations and the same word in english can mean a lot of different things.