For the first one, you can includ "that is," it's not wrong, it just sounds a bit cumbersome.
The second one, you can omit "who are," but you need to change the word order. Silly is an adjective, so it would go in front, "silly people shouldn't be..." You can do this in the first one as well if you make success, happiness, and health adjectives, "I wish you a successful, happy, and healthy year."
In the last one, the comma is taking the place of "with," so it could be reworded "He smiled with his eyes full of laughter."