I’m a cynic, but I can say this;
Happiness is the key to life? No. I don’t like that phrase. I’d much rather look at it like this; Happiness is a way of life. You ‘choose’ to be happy if possible. The key of life is to live it how you want to live it, if you can.
Laughter is the key to happiness? Yes. You don’t have to be happy to laugh. But you become happy when you do laugh.
Laugh and you’ll be happy, and everything that comes with it.