Tell me about the Germanic Tribes during the Roman Empire. How did the Germanic Tribes eventually take down Rome? Why couldn't Rome stop them, what economy drove Germanic Tribes, population in comparison to Roman Empire, etc.

There's an incredible amount of information that can answer most of your questions, some with quite good detail due to the documentation, too. Although it is mostly from the Roman's side as the migrating societies did not write down all too much during the 4th and 5th centuries.

The short answer to how they took down Rome is to start with for one, only half the Empire fell. The other half in the East continued to exist for another thousand years. Second, it wasn't necessarily due to outside forces the Western Roman Empire lost authority as they had plenty of their own issues of civil wars. Thirdly, the Germanic migrations and wars against Roman territory was over period of about 230 years; and even before then Germanic confederations had been allies and enemies with Rome. Lastly, it was really the Hunnic War against Attila that really broke the Western Roman Empire's back, the Germanic peoples just cleaned up what was left.

Rome's constant contact with Germanic tribes began with Caesar conquering Gaul, which established a border against them. At that time, the Germanic tribes were very distinct from Romans, and distinct enough from most Gallic tribes. Rome had some initial success entering Germania, establishing contact with tribes, at about 50BC. However, due to the events of the Battle of Teutoberg Forest, led by the Romanized German Arminius, the Romans decided to establish a frontier and not to conduct any further permanent conquests into Germania. At this time, although they were brave warriors, they were quite behind technologically and ideologically which led to the first part of where the Germanic tribes would be hiding out in the woods. This was because there was occasions where the Roman legions would march in to foray and raid to preemptively strike. The dense forests and harsh terrain of Germania, lack of supplies and trade to forage, and fiercely independent people led Rome to decide it just was not worth pursuing permanent conquest and occupation. Similar to why Hadrian's wall was built. Furthermore, Germania had no real cities, little infrastructure, and low population density compared to Italia or Greece. Instead as explained later, they opted for more diplomatic soft powers - pitting the tribes against each other and bribing allies. To the Romans, Germania did not have enough that would have been a net benefit to expend the resources and lives to conquer it. It was cheaper and easier to trade with them, and once in a while conduct a pacifying raid. When they did try larger operations, the Germanic tribes often fled deeper into uncharted territory.

Between the Battle of Teutoberg Forest in 9AD, there was several series of Roman civil wars over the centuries, which caused all sorts of upheaval. There was actual a period of few major Germanic wars until the Emperor Marcus Aurelius' Marcomanic Wars in 166 to 180. Marcus Aurelius spent the majority of his reign fighting them, with the result only being stabilizing Rome's borders and protecting it from outside invasion - scant few riches gained through conquest as previous Roman wars had. Throughout these centuries of sporadic warfare and relative stable borders, the Germanic tribes, especially the ones that bordered Rome, had begun to slowly adopt some Roman ways. Germanic chieftains would send their relatives (often as hostages) to Rome to be educated, as was the case with Arminius. However, one key difference that would be almost ever present on the Germanic side was that they did not have legions or professional soldiers like Rome did. The reason they could continually mobilize thousands of soldiers was because every freeman capable of fighting was expected to do so. They were martial societies led by a warrior elite. On the flipside, the aforementioned wars and civil wars that Rome had experienced meant they had manpower shortages that they caused them to be accepting of Germanic enlistees into the legions as auxillia, foederati, or even outright rank and file legion participation.

Until the Crisis of the 3rd Century, the Roman legions were able to keep their borders in check on their own. While they were still powerful into the 3rd century, their manpower began to wane as costly wars with the Eastern kingdoms and civil wars occurred. It became cheaper to just pay off Germanic tribes to be buffer territories or be an ally to Rome on the Germanic frontier, and use the Roman legions against each other or the Sassanids, Parthians etc. This all changed with the arrival of the Goths, who migrated into the Balkans in the 250s, during the middle of the Crisis of the 3rd Century. The legions managed to beat the Goths, although even Emperor Decius was killed in battle. The Goths were much less Romanised than the West Germanics, as the Goths were Eastern Germanic, and shared less influence. However, the Goths were quite quick in learning Roman ideas. Shortly after the Alemanni also invaded, along with the Franks, Vandals and other peoples in periods of about 260-270. All during the political upheaval Rome was going through fighting it's own civil wars as Emperors were assassinated and usurped. The Alemanni even penetrated into Italy. These wars were really only ended upon Emperor Aurelian reuniting an Empire split into 3, and managed to beat the Goths.

Now it may seem like the Germanic tribes were always on the move, but they were actually somewhat settled in where they inhabited. They only migrated when outside forces caused them to, or when they were on conquest. The general area that the Marcomanii and Alemanni inhabited were relatively stable for centuries. After Aurelian (and a few less famous Emperors) pushed them back to their homelands, things were somewhat quiet again until 350. Again, in 357 the Alemanni attempted an invasion while the WRE was stable. The result was a disastrous battle for the Alemanni. So what I have been hopefully explaining is that the Germanic tribes, had great difficulty in actually defeating a focused Roman field army until this point. Teutoberg was an ambush in German territory, and the few other victories were often minor or due to inability to concentrate enough manpower at that specific point in time. It was a combination of other threats, such as in the East, which was the wealthier part of the Empire, and civil wars. When the Germanic tribes had success it was often because they could capitalize on the Roman's being distracted elsewhere. Furthermore, as time went on, the Germanic tribes Romanised, while some Roman aspects Germanised (specifically the Western legions). Examples such as the spatha, more cavalry, and accepting many non-Romans into the military; which was nothing new, except many entire commands were foreign who received orders in their own language. Some particular units to note were the Batavians, who were very effective and loyal up until the Batavian revolt.

This all chanced in 376, as the rise of the Huns in the East (the ponto-caspian steppe) were pushing Eastern Germanic tribes to the West. For historians, this begins what is known as the Migration Period. It wasn't about conquest or pillage anymore, it was about survival. For a list of grievances and atrocities, the Goths came into conflict with Rome again. I forget who said it but it lead to the Goths being the "reluctant arbiters of barbarian vengeance". With practically a skeleton crew watching over the Balkans while the legions were on the Rhine and the Tigris/Euphrates, the Goths unleashed their vengeance, ransacking Thrace.