Question: Before Aquamarine showed up, Claire's grandmother told the girls that there was going to be a storm. Later, the girls learn that the storm that night was caused by Aquamarine's father getting angry. How did Claire's grandmother know that there was going to be one, unless she knows Aquamarine's father?
Answer: Because caused by mythical sea-dwellers or not, storms always have telltale signs beforehand, like darkening skies, or the wind changing temperature and strength.
This does not answer the question in the context of the movie. A fantasy situation is happening in a fantasy movie. The realistic answer is not necessarily the correct one.
Question: Why did Claire and Hailey not want anyone to know that Aquamarine is a mermaid?
Answer: The media circus that would surround the discovery of a real life mermaid would threaten the girl's goal of trying to get Aquamarine and Raymond to fall in love. It's exactly what Cecilia tries to do when she discovers Aquamarine's secret.
Question: I'm confused about the ending. Aquamarine didn't find romantic love, but she did find friendship love with Claire and Hailey. However, doesn't Aquamarine's father already believe in family or friendship love? He obviously cares about Aquamarine, since he was angry when she ran away, and he and her mother named her after a "rare and precious gemstone".
Answer: Many people treat their children like possessions. You would be angry if your TV disappeared, but that doesn't mean that you love it like it was your child.
Answer: I think her father's anger was more specific: she refused to marry the boy that he wanted her to marry, as was their custom. He probably agreed to the deal - her finding love in three days - because he expected her to fail anyway. Then she actually made some progress by developing a friendship with two humans. Apparently this made an impression on her father, even if she didn't find romantic love.
Question: When the girls first meet Aquamarine, they scream after she shouts 'BOO' to them. But the two girls already knew that Aquamarine was there, so why did Hailey and Claire scream?
Chosen answer: They are in complete shock that they are seeing an actual live mermaid. And for the mermaid to talk to them just made them even more shocked.
Answer: Most likely, Aquamarine and her father had argued multiple times, about her not wanting marry the boy that he chose for her. She was going against tradition. Claire's grandmother probably saw storm signs caused by an earlier argument. Then Aquamarine's father got angry enough to make the big storm.