[Zigûr]

1. I believe when Gandalf says "nor was there any dragon, not even Ancalagon the Black, who could have harmed the One Ring," I would argue that he is speaking figuratively. He observes that "dragon-fire could melt and consume the Rings of Power" but the One Ring, strictly speaking, is not one of the Rings of Power per se but rather a related artefact with similar but not identical properties. The same is true of the Elven-Rings. By saying not even Ancalagon could destroy it, I think it's an elaborate way of saying "it's indestructible (save at Mount Doom)." Note Gandalf's caveat about why Ancalagon could not destroy it: "for that was made by Sauron himself." It was not in the nature of the One Ring to be destroyed in that fashion. It was, after all, "a thing of surpassing potency." (Of the Rings of Power and the Third Age)

Just skipping over 2 and 3 for a bit, the answer to the "Melkor>Sauron" question lies in the answer to:

4. Why was Morgoth defeated in the War of Wrath? The answer, I would argue, is that it is because by the end of the First Age his power was spent. Morgoth "squandered his strength in violence and tyranny" (Valaquenta) and was best understood as "a tyrant (or central tyranny and will), + his agents." (Morgoth's Ring) Morgoth's power was diffuse: in the shadow corrupting Arda, in his extremely large number of servants, and in the vast projects of war and industry in which his realm was occupied. By the end of the First Age, many of his greatest servants, like Gothmog and Glaurung, were dead, and despite overall victory against the Noldor vast armies under his control had been destroyed. Melkor has originally been very great indeed, and he was still able to muster at the very end a weapon - Ancalagon's dragons - that was so powerful it could drive back the Host of the Valar, which was probably composed mostly of Vanyar, who were extremely mighty in themselves. But when that failed he had nothing left. Morgoth might have waited and recovered his power, but in his endless campaigns of war against his enemies there was never time.

I think this also explains why the One was indestructible even by Morgoth's most powerful servant. Unlike Morgoth, who partitioned his power everywhere, Sauron concentrated it in this one object. Of course it seems that by the end of the Third Age Sauron had been forced to start spending what remained of his own power in the same way, even just to manifest a body for himself, having lost two in the space of about a hundred years at the end of the Second Age.

I think Mithalwen has got 2 covered, so I'll end with:

3. Smaug being "used" by Sauron doesn't necessarily mean actually having Smaug in his army (although Gandalf nonetheless evidently considered it a possibility). Sauron was not "not really strong" during Smaug's time. He was very strong - not in the West perhaps, but Rhûn and Harad were under his sway, and while he may not have found his Ring, his enemies had not found it either. He had nonetheless corrupted Mirkwood and infested the Misty Mountains and the Grey with Orcs (the War of the Dwarves and Orcs halted this, but not indefinitely). But it comes back to this issue of areas under control. Gandalf "was troubled in mind by the perilous state of the North; because he knew then already that Sauron was plotting war, and intended, as soon as he felt strong enough, to attack Rivendell. But to resist any attempt from the East to regain the lands of Angmar and the northern passes in the mountains there were now only the Dwarves of the Iron Hills. And beyond them lay the desolation of the Dragon. The Dragon Sauron might use with terrible effect." The point was not even using Smaug as a weapon as such, but rather that as long as Smaug was there any defence against invasion from Rhûn would be impractical. The chief threat (fortunately averted in the actual war) was that Sauron would be able to unite forces from Dol Guldur and Rhûn, conquer Rhovanion and the Misty Mountains, and destroy the remaining refuges of the Elves.

That's how I see it, at least.

Crossed with Inzil but I believe we've drawn complementary conclusions!