Gimli and the other
One would think that a disaster like that would be known among the Dwarves, especially considering it was a mission to retake a long-lost Dwarven kingdom. Yet, somehow, Gimli was unaware of Moria's fall until he discovered Balin's tomb.
All he knew was that Moria had been evacuated because of something called Durin's Bane, and that it still lurks inside. And while he does know that Orcs attacked the Dwarven kingdom, it was many years ago, and so he hoped they were gone.
The Dwarves dug too deep, greedy for mithril, and disturbed a demon of great power: a Balrog, which destroyed their kingdom. By the end of the Third Age, Moria had long been abandoned by the Dwarves, and was a place of evil repute. It was dark, in dangerous disrepair, and in its labyrinths lurked Orcs and the Balrog.
In the Mines of Moria, the Company discovers what has become of them: Balin, Lord of Moria, died in Dimrill Dale when an Orc shot him from behind a stone as he stood looking in the Mirrowmere.
Their language of Khuzdul is a secret that they don't share with outsiders, so writing it on a public door wouldn't have been allowed. As such, the choice to have Moria's password be in Elvish both reflects the friendship between the two peoples and Dwarven culture.
For more than five millennia, the Balrog remained in its deep hiding place at the roots of Caradhras, one of the Mountains of Moria, until in the Third Age, the mithril-miners of the Dwarf-kingdom of Khazad-dûm disturbed it.
Nevertheless everything went well as the Dwarves were fiercely determined to take back their home, slaying every orc in their path, eventually some of Moria was reclaimed and they dwelt in the Twenty-first Hall of North end until Balin moved to the Chamber of Mazarbul, which then became his seat of rule.
Balin is mentioned by Gimli as the King of Moria, and his tomb is seen in Moria. No mention is made about the past of Moria and his expedition, and Gimli seems confident he is still alive. 2012-14: The Hobbit (film series): Balin is played by Ken Stott.
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.
Therefore, the only explanation as to why Gandalf doesn't reveal the Balrog's presence to the others earlier in the films, is that it is a plot device used by the writers and the creative team in order to increase the dramatic tension of Frodo's decision.
This particular beast was awoken by the Dwarves who dug too deep in the mines within Moria. These creatures are very large, recorded as being twice the height of an Elf with a whip and sword made of fire that never stopped burning and even appeared lava-like.
Unfortunately, the Fellowship's journey only confirmed what he had feared. Although Gimli knew that Moria could be dangerous in the book, he did not know about Balin's death in The Lord of the Rings: The Fellowship of the Ring movie possibly due to slow communication and Dwarves' perception of time.
Nobody knew exactly what had become of Balin, Lord of Moria or the dwarves that he took to reclaim Khazad-Dum. They were last heard from 30 years prior. Gimli son of Glóin and the Dwarves of Erebor did not know what had happened to Balin's Dwarf colony of Moria, for no word had come from them for a quarter century.
Though Gimli has no children, he is not the last Dwarf of Middle-earth. After the fall of Sauron, his people continued to thrive in the Lonely Mountain. Gimli made his home in Rohan, in the Glittering Caves of Aglarond, and many of his kinsfolk came with him.
Expedition into Moria
In TA 2989, Balin led an expedition in an attempt to reclaim the ancient Dwarf kingdom of Moria, hoping to re-establish Dwarven rule and to reclaim the last of the Seven Rings of the Dwarves. Though his king did give his consent, Balin and company went anyway.
It was not until the Fellowship of the Ring had passed through Moria and inadvertently reawakened the Balrog that it was finally slain in a great duel with the wizard Gandalf.
"He perceived at once that Galadriel would be his chief adversary and obstacle, and he endeavoured therefore to placate her, bearing her scorn with outward patience and courtesy.” After the Mirdain revolted against Galadriel and took over, Galadriel aided by her dwarf friends passed through Moria and came to Lorinand.
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 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.
The word “Balrog” exists in the myriad of languages invented by Tolkien for his tales, but almost always has the same definition: Balrogs are demons. There were likely only seven Balrogs. Only two have been named by Tolkien: Durin's Bane and Gothmog.
So when she allows this incredible rarity to Gimli, she essentially gives him the three hairs that Feanor demanded of her, because she has looked into his soul and found that he has a good heart and that he desires them for nothing more than to treasure the beautiful days he spent in her lands.
The inscription was a riddle (in Sindarin: Pedo Mellon a Minno.): "speak friend and enter." The answer was a password in an Elvish language that would cause the Doors to swing open. Gandalf eventually solved the riddle, remembering the Elvish word for friend, mellon. Ennyn Durin Aran Moria. Pedo Mellon a Minno.