The Pickaxe is a tool that can be used to mine ores in the mine. When you make a Copper Pickaxe and equip it by pressing E, you have the ability to mine Coal and Copper Veins. You must buy higher-tier ores such as Tin, Iron, or Adelite to be able to mine those ores respectively. Each Pickaxe can mine its current tier and anything below (eg: Iron Pickaxe can mine Iron, Tin, Copper, and Coal).
Heat the Ingots and put them on the anvil. Hold down 'Z' while looking at the Anvil and select 'axes' from the radial menu. Hit the heated ingots until they turn into a Pickaxe. This is the same recipe as the Two Handed Axe as they are variant of each other, requiring being hammered while heated and on the Anvil in order to switch in between eachother. While it is still heated, hold 'Shift' and click the left mouse button on the pickaxe to give it a quality boost. If you switch the design of your axe you will need to redo the quality. Dip the axe in the oil and bring it to the workbench to connect to grip.