Near the begining stages of the game when you fall down the hole and start exploring I walked by a path blocked by an unstable wall, what object can be used to destroy the wall, since you dont really have that much to work with in the start??

To clarify, open the inventory and double click on the pickaxe, making the cursor turn into a little circle thing, then move close enough to highlight the wall and click on it.
This works with all other unstable walls as well as gems, crystals and metals that are stuck in walls and can't be grabbed directly. Mining opportunities are found all over the place and can earn you a lot of money, so you will definitely want to carry a pickaxe with you at all times.