From what I understand, a new block contains all the transactions within the last 10 minutes. So when Alice sends Bob 10 BTC, how does this information get put onto the newest block? I guess I am wondering who collects all the transactions and then constructs the new block? Does the client facilitate this and how do we know it contains trustworthy data?
And when the block is discovered by a mining node, I understand that it tries to find a nonce which hashes to leading zeros as part of proof of work. I read that miners help 'verify' transactions. How does finding a nonce verify what is in the block? Or does the verifying refer to other nodes checking that "block + nonce" hashes to correct number of leading zeros?