The axe is a default tool so when used it wont have any effects on it. The shap axe is a consumable tool that dulls when used to cut trees, bushes and logs to clear land but will not dull when used to craft thing like peg joints. The dull axe can only be crafted into the shap axe in the work shop. The only reason i can possibly think of is to keep people from clearing to much land to quickly or to spend more time gathering resources.

Berry trees are found in the decorations tab of your building and requires berries, leafy branches and nubucks and one person if recall correctly. Once you have these drag and drop into any open flat spot in the world. Berries can be found by gathering shrubs and leafy branches are found in the leaves piled around it is luck on how often you get these items so it may take time to aquire them. The nubucks can be gotten multiple ways level up, task rewards, and sometimes the game hut or be bought with money. Once the first one is grown you can interact with it and harvest berries with a small bucket in your tool shed (not consumed) and water in your in your store house. The amount of water needed goes up the more people harvesting in a one to one ratio, so 5 people will require 5 water.