Where they not all ~10,000 BC ?
No. Agriculture and animal domestication began in the Fertile Crescent somewhere between 8,000 - 6,000 BCE. China was around 4,000, and Native Americans around 0 - 1000 CE,
However devestating the ice ages are, some areas will remain in nice and still ideal for growing.
Not enough to sustain current levels of life, or at least comfort.
Was there simple agriculture elsewhere that spread with new waves of humans/animals to the fertile creasent/China/central America?
No. The Native Americans didn't develop agriculture for around 8-10 thousand years (when the Mayan etc thrived). POpulations spread without developing agriculture. OTOH, the various type of root-plants lke potatoes were carried over as people migrated.
If so, where did it come from, who moved it, and what was society like in the area of origination.
With agriculture, domestication, and urbanization, you free up tons of man-hours of energy to things like social structures, science, soldiers and warfare...
The fact is that some hunter-gatherer cultures lived right next to agricultural without adopting their techniques. Why? No fucking clue.
Grains were originally wild and those edible were eventually found through watching animals and through trial and error/illness/death. Where did these edible grains come from?
Same way all plants come from. From plant evolution, the plant is eaten, then the seeds deposited in the fertile mound o' poo. The theory goes that this was first noticed by people who noticed that plants were growing in their toilet-ditches and garbage heaps. Also, there was a level of genetic engineering. Not on pace with today, but through generations, after a few hundred years, farming communities bred the biggest, most valuable grains - like putting a prize bull our to stud. Corn developed from a similar plant that was the size of a pinky - over thousands of years, corn grew in size. Natural selection.
Where they completely wild and only after they were well estbalished in the cresent did humans discover they were edible, or was there a long established knowledge that these plants were edible and humans migrated with them when human/plant population was smaller?
Well, the gatherers obviously knew which plants to pick, like a hunter knows what animal to hunt (or not to). As Dr. Diamond says in GG&S, his experiences with New Guinea showed that, even as basically stone-age people, each one know very well what to eat, where to find it, how to harvest it, etc.
As far as migration... certainly, along trade routes. But like I said above, conquest was faster. Alsoa s Dr. Diamond says, it depends on how long the trade lines are and the climates - a north-south route is much less efficient trade path that stifled the movement of most domestication. Africa has the sleeping sickness, preventing domestication. Only really in Eurasia do you have a long west-east trade line along similar climates allowing for more rapid spread of methods and technology.