"The child is going to school without mom."
Translation:Ребёнок идёт в школу без мамы.
With the warning that I am not fluent in Russian, I offer the following possible explanation: Russian verbs of motion come in two forms, the unidirectional (determinate) and the multidirectional (indeterminate). The former refers to a single, one directional trip, while the latter, among other possibilities, refers to habitual conduct or conduct in general. I suspect that Duolingo had a single trip in mind, while your sentence used the verb form for habitual conduct. So, I think your sentence is correct, with the meaning that the child usually goes to school without mom. But that is apparently not what Duolingo wanted. They should have provided more context. Let’s hope someone fluent in the tongue pipes in to either confirm or correct me.
In an earlier exercise using ходить as to go to school we had: Q) Yes, he is going to school. A) Да, он ходит в школу. This course has not covered aspect at this stage, but the reason идёт is used here is because it it perfective, the child is going to school without mom, it will be a one off occurrence. In the phrase 'Yes, he is going to school' ходит is used as it is a continual process, i.e. he goes to school everyday.
Yes. Here the singular feminine nominative word for mom, мама, is now the singular feminine genitive word мамы.