I think you ask some key questions...
“But how does it have value, except for everyone involved believing it has value?”
The US dollar has value because we believe it has value. We believe this because we have confidence in the US government. The currency itself is just bits of paper and metal.
Bitcoin has value among users because they value what is behind the cryptocurrency -some measure of privacy and freedom from most government controls.
“Is the value pegged in any way to dollars or any other currency of any country?”
Not pegged. The US dollar is not pegged to most currencies in the world. They float moment by moment.
“And who decided that Bitcoin miners would get rewarded for doing complex computerized calculations with more Bitcoin in their accounts; who exactly is paying the miners for their time and effort?”
Miners validate the blockchain technology by performing those calculations. This unlocks bitcoins to them. It was set up by the founder to limit the amount of bitcoin available.
The bitcoin tokens are provided to give incentive to continually validate the blockchain itself.
Best.