A villager's health is related mostly to food supply, illness, the type of job they are performing, and medical technology. Eating doesn't directly improve a villager's health.
The path you take purchasing various Village Techs depends largely upon the strategy you're using to play the game, and how your particular game is going. There are distinct advantages to each level of village tech, and choosing which one to pursue at any given point is part of the fun. If you go to the Village Tech screen and select one of the tech areas, you can tap on the Info button and see what that particular technology will do for your village. Decomposing bodies are not necessarily a problem for your island, and they will "go away" without being buried. If the deceased villager is too creepy, you should probably work on a tech that would allow your villagers to learn how to bury people.
