Would someone explain to me why I was supposed to use "alcune" rather than "qualche" here? Is qualche only used with singular nouns?
Yes, and alcuni/alcune only with plurals, unless the sentence is negated (non c'è alcuna ragazza qui, there is no girl here).
Why is not corect Qualche ragazze mangiano riso?
Qualche is always followed by a singular noun. ....so here you need to use
qualche ragazza mangia riso
Qualche is more like any and alcune is more like some/a few
The first is used in singular and the second in plurals
I used delle instead of alcune, it was accepted, but is one better than the other in this situation?