"생일 축하해! 오늘 하루 멤버들과 즐겁고 좋은 일만 있었으면 좋겠어. 맛있는 거 많이 먹기!! 항상 건강하고 행복하자." It is perfectly good as a message to someone you're friends with, but not for someone you haven't met or who is older than you. "먹기" is a cute sounding ending used mostly among children and youths. "행복하자" (-하자 used with an adjective) is something a strict grammarian might object to. But these expressions are commonly used. They have a slangy flair, making it more interesting than the more proper alternatives.