How did Europeans really conquer the Americas?

This is a huge question, one that cannot possibly be covered entirely in a single answer on a website. However, the three points you listed in your question can be addressed, and I've tried to do so below. Please keep in mind that even these could each have whole books written about them, so I'm aiming for the broad strokes here, just to give you an idea of why those points you made didn't stem the tide of European conquest.

More Americans than Europeans

The Wikipedia entry about the spread of smallpox (and numerous other sources) report that somewhere between 90-95% of the native population of the Americas were killed by Old World diseases. That's the end of the world as far as the natives are concerned. It's utterly unimaginable today. Seriously, I've seen post-apocalyptic horror movies with more conservative death tolls than that. By comparison, the Black Death "only" killed 30-60% of Europe's population, and it's still considered one of the most horrific and destructive events in Western history, and required centuries before Europe truly recovered.

No civilization in history, none, could withstand centuries of constant warfare and encroachment against multiple empires simultaneously after 90-95% of their population was destroyed. With those kinds of numbers, it's stunning that the Native Americans (or anyone in their place) could last as long as they did.

Even if there were still more Native Americans than European settlers/soldiers, (which there certainly would have been for a while), the societal and economic effects of that kind of ongoing die-off (because it didn't happen all at once) would devastate your ability to organize and defend yourself.

Relative Individual Military Prowess

I actually asked a similar question on here a while back, and the answer was very illuminating: it's not just about bullets vs arrows, it's about armor. Steel chestplates, like the Spaniards and others would have used, could deflect stone arrowheads easily. Weapons of stone, wood, and bone were no match for metal swords and shields. And while a Native American warrior might be able to penetrate European armor with an arrow or a melee weapon, they had basically nothing which could protect them from bullets or steel pikes. What use is putting a lot of arrows in the air if most of them are just going to bounce off? If you have a 50% chance of killing me and I have a 100% chance of killing you, I'm probably going to win.

However, it is worth mentioning that the Native Americans were fierce and passionate warriors, (of course, with variability from tribe to tribe). My favorite example of this is the Comanches: even today eastern Texas is much more densely populated than the west, and that is due in part to the Comanches, who basically stopped all westward expansion until the six-shooter and other rapid-firing weapons finally overpowered them.

The Native Americans had a rich and vibrant culture, but when it came to weapons production, they were barely out of the Stone Age. The Europeans had been making better weapons than the Native Americans of the 15th and 16th centuries for literally thousands of years.

American Diseases

As mentioned in the comments, American diseases did affect the Europeans (such as syphilis, which is still with us today). And the points you mentioned in your question, about relative urbanization and such, are definitely important. However, there are a couple of other things to keep in mind:

First of all, a LOT of deadly diseases come from China and Africa. Even today, the average person could easily name a number of diseases coming from Asia (such as SARS) or Africa (such as Ebola or HIV/AIDS), while I bet not many could name equivalent plagues from the Americas. I'm not an expert in disease origin or spread, so I can't tell you why, but it does seem that many more of the great plagues of history have come from Afro-Eurasia than from the Americas. So when the Europeans met the Americans, they were both susceptible to each other's illnesses, but the Europeans simply had more scary things to bring along.

And second, it wasn't an equal trade: there were WAY, WAY more Europeans coming to America than Americans going back. If a Spaniard in Mexico got sick, maybe they'd die. Maybe they'd infect the rest of the town, and more would die. But either way, Spain would be utterly unharmed. Odds are the sick people had no plans to return home anyway, and even if they tried, they might die before arriving. Meanwhile, if a Native American got sick, this was their home. It could quickly spread to their tribe, then the neighboring tribe, and so on. It was like Muhammed Ali's "rope-a-dope" strategy: America was taking all of the "hits," as far as infected arrivals, so Europe never really got tagged by any reciprocal infections. Maybe some colonists would die, but they'd quickly be replaced and the process of colonization would continue unabated.

Final Thoughts

In the end, the conquest of the Americas comes down to a single issue: it just wasn't a fair fight. The Native Americans had had their tyrants and their wars over the years, but nothing even approaching what Europe had gotten used to millennia ago. Europeans at that time were simply used to many things that were unheard of in the Americas. America had never known anything like the Roman Empire or Alexander the Great, ideals which inspired every European conqueror who crossed the Atlantic. America had never experienced (to my knowledge) any kind of religious war, a concept which had been refined into a brutal artform in Europe for centuries. America was unprepared for a devastating plague like smallpox, while Europe had had plenty of time to recover from the Black Death.

Europe was a really, really rough neighborhood (and has been for most of its history), and they'd refined the tools and tactics of war and cultural domination over centuries of bitter competition between the hundreds of factions that fill up European History books. Brutal sieges, religious persecution, forced labor, forced conversion, large-scale theft, destruction of local culture. These things were utterly unconscionable, crimes against humanity even, but they weren't terribly different from what the Europeans were doing to each other at the time, except for the scale on which it happened in the New World.

Imagine if, today, aliens arrived in orbit and pelted the entire surface of the Earth with radiation bombs, killing 95% of humanity. Then, imagine they landed in multiple locations simultaneously, and started enforcing their will with weapons we had no way of defending ourselves against. And finally, imagine that while the remnants of humanity struggled to organize and recover, more and more ships were arriving in orbit every day, bringing more and more soldiers and more and more settlers to Earth.

I could only pray that we'd last as long as the Native Americans did.