Answer: The grandexchange in varock. That's the only non combat, and non smithing way.
Answer: You can buy one at the Grand Exchange; make one yourself; or buy one at the kiteshield shop.
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The adamant battle axe and adamant scimitar are.
Grand Exchange
addy scimitar
The next level would be rune armor.
You can find this out quickly in the game itself: click on the skills icon, and click the "Defense" skill - the relevant skill for wearing most armour. In the case of adamant, the answer (for the new RuneScape) is that you need Defense level 40.