I'm glad you're asking questions. That's what is a responsible route.
It's hard to explain Bitcoin mining, but solving the problem is a way to secure the Bitcoin network. To attack the network someone would need more processing power than all the Bitcoin miners combined, which means millions of dollars or more worth of expense. As the network of miners grows so does the cost of attacking the network until it's eventually infeasible by anyone, including governments.
No data is being gathered. Absolutely everything with Bitcoin is transparent; it all happens in the clear where everybody can see all the programming and transactions. The only thing people don't know is your private key, which allows you to spend/send the coins.
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