The answer to every one of your questions is available in-depth in the following links:
FAQs: https://nubits.com/about/faqs
Introduction to NuShares: https://nubits.com/nushares/introduction
White paper: https://nubits.com/about/white-paper
If there is any question in particular you're interested in learning about in more detail, I'd be happy to talk about it.
TL;DR answers:
How is nubits pegged to the dollar? What determines the pegged value of nubits?
Through blockchain voting that adjusts the supply of NuBits in circulation. NuBits are pegged to $1.00 US as per the white paper.
What can you do with nubits? If the answer is sell it for dollars, where can you sell it?
From the front page of https://nubits.com: buying, selling, trading, transferring, saving, and creating. More detailed examples are available there too.
What is the value of a nushare? What is the value of the Nu Network? How many Nushares are there?
Currently 0.002445 USD on www.coinmarketcap.com. The supply is about 814,000,000 NSR and expanding by 100,000,000 NSR if the recent auction is successful.
What determined the amount of nushares?
One billion NSR were created to be sold to interested cryptoinvestors. The supply grows at an approximate 2% per year from PoS rewards.
What is the Nu network? What is the point in owning equity in the Nu network?
The Nu network is one blockchain that has two units: NuShares (equity in the blockchain) and NuBits (a pegged digital currency that is sold and maintained by NuShareholders). Think Apple stock and iPods. NuShareholders are in the business of offering a pegged digital currency product.