A BTC private key is used to sign tx's and prove that you own the funds that you want to spend, without a private key you cannot spend the funds that's in an address. A BTC address is used to receive BTC's, take note that even though you use your BTC address to receive BTC's, your money isn't stored in your wallet address, but on the BTC network, and anybody that gets your keys can spend your funds.
Miners confirm transactions and compete to add them into a block, the miner that is successful in doing so gets a block reward, so  because of the many miners in the network, BTC's hashrate is quite high; so for an attacker to control the network, they have to get more than 50% of the total network's hashrate, which is too difficult to happen. So miners fit it by providing security, confirming transactions and earning BTC's, bringing more of it into circulation.