Your second example:
It isn't such a big problem as you might think.
is something I might say, but I'd probably never write it. However, if you make it conform to the first rule you cited, it turns into:
It isn't as big a problem as you might think.
This new version reduces nicely without changing its primary meaning:
It is not as big a problem as you might think.
It is not as big as you might think.
It is not as you might think.
It is not as you think.
The original does not reduce gracefully:
It is not such a big problem as you might think.
It is not a big problem as you might think.
It is not such as you might think.
Which suggests that it is not a properly structured sentence.
To answer your second question, the teacher would definitely say
Could you pick me up a fruit as sweet as an apple
The second construction is technically correct (except that it should end with "an apple"), but in English we usually lead with the direct object before we modify it with a preposition. The more you separate the verb ("pick up") from the direct object ("a fruit"), the more challenging it will be for listeners to understand your sentence.
This would be especially true in a classroom where the teacher is trying to be very clear in her instructions.
I would expect her actual phrasing to be more like:
Could you pick up a fruit for me that's as sweet as an apple?