To increase happiness: look at your monsters profile and look at its favourite colour, decorate your room in this colour and your monster will become happier also if you get a moshling that will help as well. (please check other link)
To increase health: go to the gross-ery store and buy your monsters favourite food (check your monsters profile) and then go home and look in your suit case then place the food over the monsters mouth and it will eat the food. Also please add me, my character (on moshi monsters) is bananatwirl!!!!