that's English that developed some 'narrowed' meaning to the word 'seeing' - we are translating from Hebrew to English not vice versa therefore both answers (and a few more I can think of) should be correct.
And your objection applies to only one situation (relationship) not to general meaning. In that short phrase we have to translate there is no boy, man or another girl - or anybody else.
The ו in רואה makes it present tense so the correct answers should be 'the girl sees' or 'the girl is seeing' but when I wrote the latter, it said I was incorrect and told me the first was right (which it still is). Can someone fix this, please? It might confuse some people who already know a bit of Hebrew and can give misinformation to people who are just starting out.
Because of gender. ילדה is a feminine word; child is neuter. While the masculine can, and often does, include the feminine, as in ילדים, a masculine form that includes girls as well as boys, ילדה is a strictly feminine form. This gender insistence is excluded by child.