It does not matter whenther you mine copper or adamantium or whatever. The chance that you'll break your pick is the same and is calculated with each strike against the rock. It is set consistently across all ore deposits and is randomly picked vs. a base percentage.
Gem chisels/picks work in a similar way, with each mining attempt being an opportunity for the tool to break. The type of mineral deposit does not matter.
As for player-made tools, they're weapons, not crafting tools. The mining deposits are sensitive to the use of specific tools only. Copper/bronze/iron heavy picks are weapons, not mining tools, and as such they would not be able to be used to improve one's chances at mining, they won't be more durable, etc.