Translation:The girls eat so that they become women.
"afin que" requires the subjunctive conjugation of the verb, so you want this:
Je mange du poisson afin que je devienne un poisson.
I do not think so, strictly. Saying "so that they become women" means that at the end of the eating process the girls will be women, the eating process being referred to is one which stretches over years, their eating in childhood/adolescence, not a specific event. Hence the sentence is correct. Your suggestion eliminates ambiguity and improves the sentence.
"The girls eat so that they become some women" doesn't make sense as an English sentence. "Some women" indicates a partial amount of the total. In this case, we have to assume that all the girls in this sentence are becoming women. If you were to use "des femmes" in the same sentence, it would have to be "Des filles mangent qu'elles afin devinnement des femmes." which means "SOME girls eat so that they can become SOME women."
"Des" should still be in this sentence, because the number of women is an unspecified amount, so we have to put "women" because how are you supposed to know how many women there are (well, except that it's more than one)? And as for "some women," look at my answer to andy1295.
I think the issue is the use of tense. If I said in English "I study to become smart" it would be correct. If I said "I study to becoming smart" it would be incorrect. To use "becoming" the sentence would have to be something like "By studying, I am becoming smart". My brain is just about full, so I can't think what the French translations would be, but in English, to use the word "becoming", the correct format would be "By eating, the girls are becoming women" or "Because they are eating, the girls are becoming women".
Because most Duo students have limited vocabulary and less knowledge of various tenses. Some of those tenses have a quite different usage from English and require a good foundation in French.
So all examples have to be constructed from a few hundred words at most while staying in the present tense.
If your sentence that you just used were put forth by Duo, most students would get only five or so words and would be thrown by one of the verbs because of its tense.
Not to mention putting a complex sentence into interrogative form.