It's a yes and no kinda thing, last time I checked in on it. There are examples of children's toys with wheels made by Mayans, but examples of wheeled vehicles don't exist. There's an argument that they lacked suitable beasts of burden to pull vehicles (at best is a llama, which isn't really great at pulling), so that might be why, but that's ultimately conjecture.
You're right that Llamas are South American (though they weren't always - the fossil record shows Llama-like animals as far north as the southern states ~20K years ago), but mexico is so much more than just tropical jungles! Some parts see snow every year, and there are piles of mountains all over the country. It's such an incredible place.
No; a conventional wheelbarrow rests its weight on a wheel at the front and on the human holding the handles at the other end (since it's impossible to balance on the front wheel).
The sailbarrow has a large central wheel that bears the weight, relieving the human of the need to personally support the weight of whatever's being carried.
In the case of the Chinese wheelbarrow, that is correct, but the sail is an improvement added later to the existing conventional design of the region and era which happened to use a central wheel.
I'm no expert on international wheelbarrow histories, but assume that the term "sailbarrow" being so general applies to any wheelbarrow having a sail. The historic precedent of the Chinese incarnation is literally their conventional wheelbarrow with a sail added.
I assume the same approach can be (and probably has been) used on any wheelbarrow in appropriate conditions.
It's a domestic species, just like, say, modern cattle are domesticated aurochs. The wild equivalents are the guanacoes. They may be physically very similar, but they're different behaviourally.
There was civilization in the Andes for thousands of years before the Inka. We just know little about them. Likewise in the Maya homelands.
People who live in Peru and study the ruins distinguish three megalithic stonework traditions, with the Inka the least sophisticated. The Inka's predecessors routinely handled rocks of tens, and up to hundreds of tons, slicing them into non-convex polygonal shapes and fitting them like puzzle pieces. The Inka worked only much smaller rocks.
Originally, the king was the Inka. No name for the civilization he ruled has surfaced.
IIRC Viking used logs as well to transport their ships between rivers, so they can raid the usually very surprised towns and vilages downstream, especially for rivers going south.