When Emma leaves, is she still a mermaid?

Yes she is.

Yes. A mermaid can only lose her powers permanantly if she is in the Moon Pool when the planets all line up with the full moon. This happens once every fifty years. The last episode Emma was in, season 2 finale, this specail full moon occured. Emma wasn't in the water. The pushed चालट, चार्लोट, शेर्लोट in, and she लॉस्ट her powers, just like her grandmother, Gracie. Emma couldn't have लॉस्ट her powers. She is just traveling.

Emma lives after the episode 1,no.

I think she gives up being a mermaid before she moves.Sorry if i'm wrong.

I would say YES!!!
she is just traveling with her parents!

I think she is still a mermaid because i think she's supposed to be in season 4 and there is also gonna be a merman and i also know that in the last episode of season 3 called the GRADUATION Bella, Cleo, Emma, Rikki and Lewis all come back