1. It seems that each Ainu was given a certain amount of power to begin with. However, there are appearences of their power rising or falling. For instance, Melkor lost much of his power by corrupting other beings with it, and the Balrogs lost power by being corrupted by Melkor and having to stay in one form. As mentioned, Sauron was able to increase his power by pouring some of himself into the ring - "externalizing" it in order to achieve its greatest "potency" (Letter 211). Saruman also loses power by overstepping his limits as an istar and turning to evil, for which Gandalf removes him from the order, defeating him. And it seems that Gandalf recieves an increase in power (as opposed to only ability to express his power) when he returns from death.
2. Power is indeed more than just brute strength, both here on Earth, and notably in Tolkien's world. Tulkas himself is called the strongest of the Valar, but he is not even included in the Aratar, or eight most powerful Valar. Wisdom, talent, and leadership probably go into it. Also, power doesn't always determine defeatability or the victor in battle. Melkor is called the most powerful Vala, but he is banished. Saruman is called the most powerful Istar, but he fails to Gandalf who is weak and scared. But Gandalf is humble, and one of Tolkien's great themes is the enoblement of those with humility and commonness.
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"He was sent by a mere prudent plan of the angelic Valar or governors; but Authority had taken up this plan and enlarged it, at the moment of its failure."
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