Alternate history - What if? Roman Empire and Battle of the Teutoburg Forest

[Tran]

Brief description of the battle:
The Battle of the Teutonburg Forest took place in the year 9 A.D. when an alliance of Germanic tribes led by Arminius, the son of Segimer of the Cherusci, ambushed and destroyed three Roman legions led by Publius Quinctilius Varus.

1. Had the Roman legions manage to defeat the Germanic tribes, will it create long-lasting effect in Central Europe, Roman Empire, and perhaps the whole Europe? Was it even possible for the Roman legions to won? Or were the Romans just doing the impossible, given the fact that they venture into unknown territory, very well-known to Germanic tribes and Arminius, who in this case probably lure the Romans into the trap (initially Arminius accompanied Varus)...?

There were of course plan to again invade and attempt to crush the Germanic tribe, but these were pretty much unsuccessful, which I will quoted from Wikipedia:

"...Though the shock at the slaughter was enormous, the Romans immediately began a slow, systematic process of preparing for the reconquest of the country. In 14, just after Augustus' death and the accession of his heir and stepson Tiberius, a massive raid was conducted by the new emperor's nephew Germanicus, followed the next year by two major campaigns with a large army estimated at 70,000 men, backed by naval forces. After initial successes, including the capture of Arminius' wife Thusnelda, the army visited the site of the first battle. According to Tacitus, they found heaps of bleached bones and severed skulls nailed to trees, which they buried, "looking on all as kinsfolk and of their own blood". Burial pits with remains fitting this description have been found at Kalkriese Hill.

Thereafter, however, Germanicus suffered two devastating defeats, and withdrew to his original positions on the Rhine, Lippe and Ems. A further, even more massive invasion the next year was inconclusive and ultimately unsuccessful..."

Now another question:

2. Let's say no matter what the odd, the Romans did win at Teutonburg Forest. Will they eventually continue their expansion deeper into German territory?

3. If the Romans did manage to conquer the area, which is present-day German, what impact will it has to the whole Roman Empire? The Romans might after all gain access to Denmark, and the Baltic sea, not to mention natural resources in the region. Perhaps the Empire will live much longer, or...shorter?

4. And let's imagine the Empire eventually collapse too, what do you think the geopolitical situation of Europe from around 1800s to present-day look like?