To do the middle door math puzzles, you light up the lights on the same row and then do the math.
After you go on the elevator you can use the rust remover, but not on the telescope.
I skipped the Whack-A-Troll game. It's about being fast with the mouse and adventure games aren't supposed to do that. If you are fast you can try it without hitting any red trolls though.
The game on the door at the bottom of the well is also for fast mouse users. But an important point is that this is the same well you saw outside the house.
When you get the telescope you can use it somewhere in the cottage.
The club clue is a matter of subtraction.