Will they make new death note episodes?

Answer 1

No , there is "Death Note Relight (special)" ;

"Plot Summary: See through the eyes of a shinigami. Light and L battle over the Death Note and now you can see what the story looks like from Ryuk's point of view. When the shinigami Ryuk drops his Death Note purposely in the human world, he had no idea that a human would go as far as Light did who picked it up. With the Death Note in hand, the genius high school student Light Yagami after testing the Death Note and realizing it's true potential vows to rid the world of evil, and when criminals begin to drop dead, genius detective L steps in to track down the mysterious killer known as Kira. An epic battle of wits pitting one brilliant mind against another unfolds in this amazing redesigned version of the first half of the original series. " ~ Anime News Network