In the end Tolkien stated that there were probably "at most" seven Balrogs: In the margin my father wrote: 'There should not be supposed more than say 3 or at most 7 ever existed. '
In Tolkien's later writings, he made note of the fact that there could not have ever been more than three or seven Balrogs. In another early writing, there was a Lord of Balrogs named Lungorthin.
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.
As a Valar, Morgoth led a whole slew of Balrogs in the First Age, but because Sauron was only a Maia, the Balrog would have had no loyalty to him. He was his own master in Moria, and no Dark Lord was going to ruin that. Thus, if he really wanted to recruit the Balrog, Sauron would have had to dominate it first.
Yes, Sauron is more powerful than the Balrogs and was the greatest and most terrible of Morgoth's servants. The balrogs were beings of immense power as they were previously Maiar, essentially angelic beings born beyond the constraints of the mortal world.
In the end Tolkien stated that there were probably "at most" seven Balrogs: In the margin my father wrote: 'There should not be supposed more than say 3 or at most 7 ever existed. '
The most powerful of all the Balrogs, one of the chief servants of Melkor, who held an authority hardly less than Sauron himself. A wily commander and fearsome fighter, Gothmog was often accompanied by others of his fiery kind, and at least in the Nirnaeth he had a personal guard of dozens of Trolls.
Smaug could easily have cut through the armies of Mordor, and delayed the invasion of Middle-earth by years. So it wasn't in Sauron's interest to take on the dragon, but that doesn't mean he saw it as a lost cause, as he fully planned on creating an alliance.
Smaug was the last of the great dragons, thus ridding Sauron of a possible powerful ally. Beyond this, all the rest of the dragons in middle earth supposedly only lived far to the north; being now a lesser race, the logistics of bringing them to bear, particularly in the southern campaigns, would be unlikely.
Sauron was the mightiest of all Morgoth's servants, so he feared none of the other servants of Morgoth. Not orcs, not trolls, not dragons, not Balrogs.
The movies didn't show it, but the Balrog all but defeated Gandalf in a battle of spells. So, the bottom line is that some brutish beast like Smaug (regardless of his size) wouldn't have been a threat to a Balrog. The only thing that could save Smaug would be his wings -- if he flew away in full retreat.
We are not told whether Sauron was aware of the Balrog's existence until then - certainly the exiled Dwarves had not recognised what kind of creature Durin's Bane was. It appears that the Balrog acknowledged Sauron's authority, if only because it allowed his creatures to remain in Moria.
From this point on, up to the year of the War of the Ring in 3018 there is a cohabitation of the Balrog and the orcs for 538 years! Certainly Sauron knew of the existence of the Balrog (especially at the point when his orcs entered Moria), and the Balrog seems to have tolerated the presence of Sauron's orcs.
By my understanding, the Balrogs were seen as undefeatable up until the battle of Gondolin, when up to eight were slain (3 (?) by the House of the Hammer, 4 by Ecthelion & 1 by Glorfindel), depending on the account read. Gandalf obviously also kills Durin's bane in Moria during LOTR, bringing the total up to 9 (?).
The fall of Gondolin and the fall of Troy
The Elf Ecthelion leads the charge against the Orcs, and fights Gothmog, the greatest Balrog; they wound each other and both fall into the king's fountain in Gondolin; both drown.
For more than five millennia, the Balrog hibernated in his deep hiding place at the roots of the mountains in Khazad-dûm. He remained undisturbed throughout the Second Age and most of the Third, before the mithril-miners of dwarf-King Durin VI awoke him in T.A. 1980.
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.
Although both the Balrog and Smaug are creatures of fire, and Gandalf is able to match them thanks to the power of his fire ring, defeating the Balrog takes far more spiritual prowess, which is why Gandalf is able to essentially 'level up' and comes back as Gandalf the White, whereas defeating such an immense physical ...
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.
Galadriel's rejection of Sauron clears the way of Celeborn's return. But we're going to need some idea of where he's been since he was lost in the war against Morgoth. It's strange that Galadriel spoke so often of her dead brother but only once about her dead husband.
He was also able to sway many nations of Men, such as the Easterlings and Haradrim, to his side. Next, Sauron sought to bring the Elves into his service, so he disguised himself as Annatar, Lord of Gifts, to seduce them. The Elves helped Sauron forge the Rings of Power.
Lack Of Fidelity To The Source Material
Perhaps because the show had none. There wasn't even a hint of Tolkien in this mess, neither in spirit or in a basic adherence to the details of Tolkien's writing and established lore.
The Eagles came to help them, but Glorfindel fought the Balrog alone upon the pinnacle of a rock. Both died after falling in the abyss, and their duel is sung of by many songs.
Ecthelion killed three Balrogs and his sword did "hurt to their fire". However, dragons reinforced Melkor's army.
Street Fighter X Mega Man. Balrog appears as one of the final bosses on Street Fighter X Mega Man. His weakness is the Mega Buster and the Soul Satellite.