Smaug hunts for the thief outside on the mountain, but eventually comes back to his lair to sleep. The dwarves turn to Bilbo for leadership. He decides to go back down to Smaug and see if he can find his weak spot. Bilbo is invisible because he is wearing his ring, but Smaug can smell him.
Peter Jackson certainly makes the assertion in the theatrical and extended editions of the Hobbit movies that Smaug and Sauron are not only well aware of each other, but are planning to ally with each other. Smaug even seems to have detailed knowledge of Sauron's coming plans.
While it could be down to simple nerves, Bilbo was hesitant to give the dragon his full name. He was well aware of the destruction Smaug could cause and didn't want to give him any hints as to where he may live.
Perhaps he was intimating that the dragon was already in league and corrupted by Sauron. Or perhaps, he was suggesting that this was a soon to be possibility, using the eye as a metaphor to foreshadow a future alliance. Or perhaps he was suggesting that Smaug's evil was akin to Sauron.
How did Smaug know about the hobbits of Laketown? There are no hobbits in Laketown at that time. Smaug could smell dwarf and he was curious about this apparently invisible being, Bilbo the hobbit, that was running around his bedchamber.
Smaug did not know that Bilbo had the one ring. Unlike the Nazgul, Smaug couldn't detect the presence of the ruling ring. He had no way of knowing that Bilbo had it, was using it, or that it was the power of the ring that made it impossible for Smaug to find Bilbo. Smaug's fire could not destroy the one ring.
Smaug's ability to speak, the use of riddles, the element of betrayal, his enemy's communication via birds, and his weak spot could all have been inspired by the talking dragon Fafnir of the Völsunga saga. Shippey identified several points of similarity between Smaug and Fafnir.
He was only worried about finding the Ring, and he already had plenty of servants to do that for him. So, in short, the power that Sauron would have gained by recruiting the Balrog wasn't worth his time.
He lost even more power at his defeat at the end of the second age to the last alliance. So, War of The ring, Sauron would of only had the power to seduce Smaug with promises of greater fortune and power. He wouldn't of been able to physically or mentally command him.
Sauron allied with Smaug and intended to use the dragon's powers against the people of Middle-earth. But before that could happen, Smaug was slain by Bard the Bowman.
Posted on Reddit by user applecub, the theory posits that Legolas' name slipped Frodo's mind since their introduction was brief and overshadowed by the daunting task of destroying the One Ring. By the time they reunited in Rivendell, Frodo didn't ask Legolas for his name to avoid offending him.
TL;DR: The Ring would've used Smaug's greed to control him, making him raze Middle-Earth, and then corrupt him to such a point he wouldn't be able defeat Sauron, giving the Dark Lord control over the land.
This is because Frodo's mind was distracted with the gravity of his mission when he met Legolas so he completely spaced during their introduction.
Smaug's dragon-fine would not have been hot enough to destroy the One Ring. The malevolence that Sauron put inside of the Ring could only be destroyed in the Cracks of Doom, so Frodo was compelled to make the journey to Mordor.
Smaug was the last named dragon of Middle-earth. He was slain by Bard, a descendant of Girion, Lord of Dale.
Smaug is named "Slag", the Ancient Monster.
So, one glimpse into Smaug's eyes and the Balrog falls under the spell. Even if it's just for a second—a moment of hesitation or distraction, it'd be enough. Smaug would snatch up Durin's Bane and gobble him up with his sword-sharp teeth (and we know swords can kill Balrogs).
Gandalf was scared of this beast because he knew how powerful it was since it was a Maia like himself, but it was purely evil.
Gandalf absolutely could have killed Smaug in a one-on-one fight. The grey wizard fought and defeated the Balrog of Moria, and a dragon was a lesser evil than that.
The main difference is that, in the books, they were forged after the other Rings, not before. This means that the three Elven Rings weren't imbued with Sauron's malice, making them the most powerful among the Rings of Power — and the most coveted by the Dark Lord.
He is afraid that if he did, it would corrupt him and make him just as bad as Sauron since Sauron put so much of himself and his evil into the One Ring. Gandalf's fears are definitely reasonable. Even though he and Sauron are equal, power-wise, Sauron is evil while Gandalf is firmly on the side of good.
No, Balrogs do not serve Sauron. Similar to Sauron, Balrogs are Maiar, powerful spiritual beings second only to the Valar themselves. They were corrupted by Melkor's evil before the first age and were made into Valaraukar (Demons of Power). They very strength and wills were bound to Melkor.
Smaug is red and gold, with fiery breath, sharp claws, and a hide as strong as a diamond. Bilbo is horribly afraid, but he works up the nerve to take a single golden cup from one of the piles.
The dwarves turn to Bilbo for leadership. He decides to go back down to Smaug and see if he can find his weak spot. Bilbo is invisible because he is wearing his ring, but Smaug can smell him.
Smaug calls Bilbo a thief, and he is accurate in his judgment.