hi! direct responses to your specific questions is definitely welcome, but you may be interested in previous discussions on just this question. I've been hoarding these with a mind to creating a new FAQ section; it hasn't been pared down yet, so hopefully its not too overwhelming ...

In general

• Who invented the bow and arrow?

• Was the bow and arrow invented once, or many times across human history?

• What society first used the bow-and-arrow? And did the technology spread or was it largely discovered and developed independently across the globe? Lastly, were there any major civilizations that did not employ the bow?

• Did the bow and arrow develop independently in the various cultures across the globe? If so, why does the design seem so universally similar?

• Did the bow and arrow migrate around the world with moving peoples or was it invented independently by hundreds of different societies?

• How come every civilization - even the secluded Sentinelese - discovered/invented bows and arrows?

In the Americas

• How long ago did Native Americans settle in North America? With no contact with Europe for centuries, did they invent the Bow/Arrow independently of the lords of Middle Age Europe?

• Did the bow and arrow develop before the land bridge between Alaska and Russia disappeared or did people in Eurasia and the Americas create the bow independent of each other?

• How did Native Americans develop bow-and-arrow technology?

• Did the Native Americans have bow & arrows by 1000BC?

• Is it just a coincidence that both native americans and europeans had bows before the columbian exchange?

• When were the first bow and arrows used, and how did many cultures develop them without ever coming into contact with each other?

• Why was the bow and arrow design used throughout the world even when they had little contact with each other?

Down Under

• Why did the Australian aborigines never invent bows and arrows? Why did nobody else invent the boomerang?

Note: despite the pile of posts here, this question is actually a good fit for /r/AskAnthropology, so take a look there too