Yes, taxable scholarship is unearned income*, and is subject to the "kiddie tax", wherein a portion is taxed at the parent's marginal tax rate. You will be asked for parent income.
Yes, for tax purposes, a step parent is the same as a biological parent. If you file a joint return, use the 1st name listed on the joint return. If you claim her on a separate return, yes use your info.
*Scholarship income is unearned for purposes of the kiddie tax but treated as earned for purposes of calculating the student's standard deduction (earned income + $350, but not more than $12,550)
