I'd like to provide a partial answer to just the first question, if that's okay.
Corn and potatoes were really big ones, among other crops. It may sound odd to consider those a "technology or innovation," but they did not occur in their modern form, or really any form most people would consider suitable for human consumption, in nature. They had to be selectively bred over millennia in what was essentially a slow process of inventing new crops, and they've become very important foods outside the Americas. Most modern crops have of course been bred selectively as well, but corn and potatoes are some of the most outstanding products of agricultural innovation.
Here's a writeup dealing with corn's evolution:
http://learn.genetics.utah.edu/content/selection/corn/
And here's a journal article on research into the potato's origins: