It took me a bit to figure out what you were trying to say, so for that reason I definitely would write out "2015," or just use "new year." A typical wish would be for "a happy and healthy new year." I would say "healthy" rather than "healthful." Food can be both healthy and healthful, but people are healthy.
As for your final question, if I were to use only the last two digits, I'd put an apostrophe in front of them, otherwise it's just the number 15, not a year.