You can get hints in game for missing tfs if you go back to teh forest where you started.

But if you want some hint: You need to find some item in town and use that item in your forest home once you bought the lake extension.

For the cat quest giver.
You can find her in the northern part of town in a house. If you can't acces the northern part of town yet, the quest is not doable at the moment.

Hope this helps^^

Sorry i dont know if i understand the question right.

I guess you looking for the fireplace/chimney to climp up, in the present, after you got it repaired, in the past, and use another time gate on the higher floor to get back to the past.