Is this a special case where you can use 'ở' and 'trong' at the same time? Seems redundant.
No, these two words are actually quite frequently used together. In Vietnamese, two synonyms are in some cases used together.
Could you omit 'trong' here? Or is it needed?
This may be 'quite frequent', but I'd say in almost every sentence here on DL use both together at your peril.
Would you use in for cases like "nhà", "toà nhà", nhà hàng, khách sạn, etc?
Doesn't have "lớp học' in the suggestions.
Yep ... answer requires "lớp học" but suggestion is "lớp".
Now lớp học is in de suggestions. However, if you go by the suggestions only, đưa trẻ ở lớp học would be a valid translation. Not accepted though.
why can LA not be used here instead of DANG?
"Là" cannot be used because "ở" is the verb in this sentence. "Là" is used to describe the subject, "ở" is used to locate the subject.