Explosion of an exploding rock does not cease the smoke from puffing and therefore an exploding rock can explode again if it were mined again or mined by another player.
Pickaxes can be fixed by Nurmof in the dwarven mines and at Bob's Brilliant Axes in south Lumbridge as well as at the battleaxe shop in Port Sarim. There is no charge for bronze, iron and steel pickaxe repairs, but there is an escalating fee for pickaxes made of mithril and above. Note that only damaged pickaxes can be repaired... a broken pickaxe that has a lost handle cannot be fixed by the NPCs. To remedy this situation, you must use the pickaxe handle (not to be confused with a wood axe handle) on the pickaxe head to fix it.
This event serves the purpose of discouraging macroing by players in RuneScape, and was instituted as a preventative measure by Jagex. It is one of the many counter-bot measures they have placed on activities that require long work, like Fishing and Woodcutting.