they're the same
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Yes, chainmail armor is better than gold. Gold is the second worst armor after leather.
You can buy chainmail armour from villagers and you can also kill zombie with chainmail armour on them but its a rare drop so don't get excited thinking you will find one. You can also find chainmail armour in the creative inventory. With mods and TMI (Too Many Items) you can craft them the same way as other armors but with "Fire" instead. That's cheating, though. :)
No, Diamond is the strongest, followed by Iron. Chain is next, offering only a tiny amount more protection than gold. In terms of durability, chain is the same as iron, but diamond again is the best.
You just cast them like any other mage, select them from her spell menu. Be aware that mages can't cast spells while wearing anything more than the lighter pieces of armour. Normally a pure class mage can't actually equip such things, but the rule applies to dual- and multi-class characters too. Imoen is a Mage/Thief, so she can wear armour like chainmail, but doing so will disable her spellcasting abilities. Better to stick with things like Shadow Armour (+4 Leather Armour) or special Mage-friendly armour like Bladesinger Chain.
Use Iron Ingots on an Anvil in Minecrafft 1.4+. (It requires XP)