Question: Why did Carla put on the red dress when she was going to take over the role of Eliza in the play, since the first act started with the outfit Lola was already wearing?
Answer: Lola mentions her mum taking her allowance in August or September. That means they're in the month of July which is summer break for America.
She's being dramatic. It's spring in New Jersey during the movie, so it's probably April/May and she says "I could really use the money now mom! Can't you take it next month or...September?" Indicating that September is a ways in the future.
Question: What happened to the two girls in Dave's crew? They were at all the practices, but not in the finals.
Answer: When Dave's crew went to the finals they wanted to bring the best dancers in their group, so they apparently decided that the two girls happened to be the least strong dancing wise on his team.
Question: How much of her own singing did Hilary Duff actually do in the movie?
Answer: All of the singing that Hilary Duff did in the film is her own. This is stated in the credits of the songs she did.
Answer: My only guess is that she had to make sure the dress fit before the play, or adjustments had to be made on the dress so it would fit her.