Your villagers will begin to produce tech points faster as they gain skill at research. Master scientists produce more tech points than less skilled scientists. Also, as your population grows, you should be able to put more of your villagers at the research table, especially after you have discovered fishing.

Clues to the puzzles (except for puzzle 12) can be found by dragging one of your adult villagers around the island and by watching what they're curious about. I suggest dragging a villager around the village after every tech purchase, to see what new thing(s) they can work on.