For the first item, the materials in question should drop from puyos of different colours, though I'm not entirely sure about where these drop, don't think you can just farm any low-level puyos. You should probably look for puyos in the higher level zones you've been to and they should drop it, I believe.
For the second item, these are mostly materials you get from mining. In the third small village, you can go into the mines with a pickaxe and mine these materials or go into the area where you can go lower and lower to pick items up from the floor to increasingly stronger enemies. Red Ice, the fourth material, is one you can get in the forest with the fairy village, if I'm not mistaken.
I'm not entirely sure about the information for the first item, I'm just going by the description of the materials I translated, but I think that's how you can find the stuff. If not, I'm not really sure myself, give it a try unless someone else knows.