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Yes, somebody could use bitcoin to transfer wealth just as you described.
How the currency conversion rate is determined is by supply and demand, just like any other thing that people buy. If lots of people buy bitcoin, demand increases, and vice versa. Price fluctuates based on changes in demand. The supply increases slowly and steadily from mining.
So the exchange rate isn't determined by any one person or party, it's determined by the behavior of anyone selling or buying bitcoin.
No, not at all. As others have pointed out, the rate of transactions is and has been increasing. https://blockchain.info/charts/n-transactions
And the number of estimated users is and has been increasing. https://blockchain.info/charts/n-unique-addresses
Bitcoin has great potential aside from just being a currency. It allows for digital assets and smart property. You can also prove that you had a document at a specific time. You can make deposits without even trusting who you're making a deposit to, among many other interesting applications in smart contracts.
As a currency, bitcoin is great for developing nations. Many people have access to a computer or smartphone and internet, but not a bank or credit card. Bitcoin allows these people to securely store value and transfer it to anyone in the world with little fees. Immigrants can use bitcoin to send wealth back to their families in a developing nation very inexpensively and efficiently. People in developing nations using bitcoin won't fall victim to too much inflation
So long as the 51% of the bitcoin network is not controlled by a malicious party, it is more predictable than ordinary fiat. The rate of increase in currency is known and agreed upon (one block every ~10 minutes, block reward halves every 210,000 blocks). Users can make transactions of arbitrary size with little fees without trusting any third party. So long as a user keeps their key secure, their bitcoins don't go anywhere.
I think bitcoin is fantastic and will probably continue to grow as more applications are discovered. It is an extraordinary technology and has much potential.