H₂O: Just Add Water/WMG
Byron and Miriam were abducted by aliens at some point between season 1 and season 2.
And the aliens probably erased everyone's memories of their existance as well.
Byron secretly knew that Emma was a mermaid.
He may have seen her mermaid form during Emma's father's birthday party, while Emma was under the influence of the full moon. Figuring that it was supposed to be a secret he didn't tell anyone. Although it was only after the episode where he asks Emma to help him beat Zane in a swimming competition that he figured out how the transformation works.
Julia was the only one of the previous three mermaids who kept her powers.
Miss Chatham reveals that she gave up her powers, and it's implied that Gracie did so as well. However, we never learn if Julia did so as well. Out of Cleo, Emma and Rikki, it seems that Rikki is the one who enjoys being a mermaid and having special powers the most. Since Julia apparently was somewhat similar to Rikki, it's possible that Julia chose to keep her powers.
This is one of the reason why they were destined to be Teen mermaids before the show's beginning, since the said latter 3 could be their Japanese cousins. Another is Aqua Regina already had it planned for them after the 1st 3 Mako Island Mermaids.