To answer your first question: yes, the odds were very much against Napoleon during the Hundred Days, and most historians consider the likelihood of an eventual French victory low - but the French military position in 1815 was arguably actually better than it had been in 1813 and 14.

As you note, many soldiers died in Russia, but many more were taken prisoner, and those veterans, often fired with a hatred for Russians in particular due to their treatment as prisoners, were repatriated after Napoleon's abdication in 1814 and were therefore theoretically available for the defense of France in 1815. In the event, not many were mobilized before Waterloo, but the plans were there. The Coalition's armies had been moved home and begun to disband; the Russians had been at France's frontiers in 1814, whereas in 1815 they were back in Russian territory.

Similarly, the political coalition against France was much more fractured in 1815 than it had been in 1814; the issue of Poland, and how best to partition it, was one that the Congress of Vienna could not satisfactorily resolve, and worries about Prussian and Russian expansion led to quiet alliance-building between Austria, France, and Britain in case either power tried to force the issue.

Ironically, it was Napoleon's own return that solved these problems for the Coalition - the political will to remobilize came quickly when news of his return arrived, and since the heads of government and chief diplomats of the major European powers were all in Vienna, it was simple for them to quickly suspend their differences and concentrate on Bonaparte. The fact that they refused to recognise the legitimacy of Napoleon's return helped splinter his support in France; previously, all had recognised him as the legitimate ruler of the French, even if they hated him, which meant that French patriotism, especially among the burgeoning middle classes, for a long time was identified with support of Napoleon.

The Congress' proclamation that they were not at war with France, but with Napoleon, personally, undermined his claim to speak for the nation, and the fact that Coalition forces didn't cross the border until Napoleon did, since they were technically not at war with France, prevented him from successfully portraying himself as France's defender and instead made him appear a warmonger and criminal to many of his own people.

As to what made Napoleon an object of such devotion: on a personal level, he remained a highly charismatic individual throughout his life, able to inspire great personal loyalty. Further, the nature of his rule - that he was, in many ways, a soldier first and a ruler second (although it should be noted he was enthusiastic and detail-oriented in his rule just as he was in his soldiering) - meant that the army in particular held great loyalty to him. After all, he'd given French soldiers victory after victory. Politically, he had managed to align himself somewhat with the ideas of progress and rationality expressed by the French revolution, even if many correctly noted that he was less concerned with liberty.

The restored Bourbon monarchy hadn't done a whole lot to make itself popular, either; it had stripped the army of its flags and eagles, which, while symbols of a Bonaparte regime, had also become symbols of the army's professional pride. Many regiments had successfully carried their eagles out of Russia and back across Europe, and were now ordered to melt them down as traitor's symbols. The King also raised taxes, doubled down on the repression of political speech that had been a facet of Napoleonic rule, and in general did little to endear himself to the middle classes, the new Napoleonic aristocracy, or the common people.

However, there was still significant opposition to Napoleon's rule. While the army as a whole rallied to Napoleon, several prominent officers - who had served their entire professional careers under Napoleon - refused, and went with the King into temporary exile. Some did this due to a feeling that Napoleon was serving his own vanity ahead of France, and others because they refused to forswear the oath they had sworn the King the previous year. The Vendée erupted into almost instantaneous revolt, and Napoleon had to detail significant forces to keep this and other insurgencies contained. The middle classes never really came round, despite Napoleon's attempt to court them with a new constitution. Given this lukewarm support at home, a victorious war was really Napoleon's only option - hence the roll of the dice in Belgium.

Sources:

Swords Around a Throne: Napoleon's Grande Armée, by John R. Elting

Waterloo: four days that changed Europe's destiny, by Tim Clayton

The Legend of Napoleon, by Sudhir Hazareesingh