Nope, you have to mine for diamonds with an iron pickaxe.
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You don't.
The fortune enchantment increases the amount of diamonds, lapis, redstone, coal and emeralds you get from each ore block.
It takes 26 diamonds to make the armour and 11 for the tools, that's 38 diamonds in total.
Fortune enchantment in Minecraft means that the drop rate of items is multiplied. This includes items dropped from blocks including coal, diamonds, glowstones, and redstones.
You can make a diamond sword in Minecraft by placing two diamonds above a stick in the crafting table.