Sick villagers won't get better unless you heal them. If you drop a villager on a sick villager, they will heal the sick one. That works only for sick villagers, and not weakened ones.
If you have any children, you can drop them on mushrooms to get enough food until you have enough tech points for the next level of farming. The berry bush will not support your villagers for very long.
Certain Island Events can give you a tech levels, but you can't count on them, and there's no way to get farming tech except by earning tech points.
As your researches gain skill, they will start to get points faster. It takes more than 6 hours to have things really take off, though. You can always read the
Strategy Guide to get some general help with the game. Good luck!
