Does anyone know do the villagers eat on there own or do I have to drag each one over to the food in order to feed them?

You can feed them, but you don't have to - they will feed themselves.

Villagers eat on their own, but there may be times that you want to drag a villager to the food bin in order to feed them: If they are in a "weakened" state, eating can make them feel better (after one or a few tries you will see a note at the bottom of your screen saying something like "your villager feels better after eating")

I have a weakened villager and I've feed him several times even after it said he feels better, but the health bar continues to decrease. How do I get his health bar back up?

If the villager is elderly, he may not regain his health. Eating does improve their health, but only a very small amount. You can put him on a less hazardous occupation, such as farming, which usually helps recovery.