It all depends on the context, which the writer has not made perfectly clear in this case. 1 - a child often has two parents (the writer coud have used children's as in #2 2 - (see #1) 3 - offspring is a singular word that can refer to more than one child; hence offspring's is correct.
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tinanam0102Hi Philip,For the last sentence, do you mean:The administrator asks parents to sign the pamphlets when the student has completed the assigned work. ThanksTNYes, or even simplify it to: 'sign the pamphlets once the work has been completed.'