I have solved all the puzzles and am now just running the game to see what happens. I know I don't need research skills anymore but what about building? I have quite a few children now but don't think they all need to be farmers, what will happen if I don't check any skills? Will they learn on their own when they get old enough?

If a child is born with even the tiniest bit of innate skill, they will continue to practice that skill once they reach working age - 14 years old - even if you don't set a preferred skill for them. Of course, that will only happen if they have something to work on in that profession. I've seen 14-year-old scientists actually working at the research table, even though all of the Village Tech was at level 3 and the adults had abandoned the research table. Youngsters with building skill will work on any building projects that are available, which is typically only the occasional debris event that late in the game. If a child is born with no skill, you will have to train them in something or they will just sit around, pace back and forth in village center, or complain about things!

Thanks for the tips.
I've always selected the skills my villagers should have, and trained them on them - got them to do the skill. Maybe I'll try the game where I don't pick what skill they have, except possibly for breeding. I've solved all the puzzles, so I'll see how this goes. I'm very interested in keeping my village going, so I'll have to watch it, to make sure they have food and healers!