Since you have attained the highest levels of Village Tech, your scientists have no reason to continue researching. Any villager who has no experience in any skill other than research will do as you describe. To get them to do productive work, you have to retrain them in another area, such as farming or healing.

Sometimes it takes awhile for Puzzles 10 and 11. The villagers that are breeding are doing exactly what's needed for Puzzle 10. Just be patient. You can complete puzzle 12 before the other puzzles, so that's something you could do while you're waiting.