I try to help a bit on the question, there is more than it seems:
1.) transactions are basically a transfer of value from one address to another address. When a transaction is sent to you (to your address), then it should have a confirmation in one block, before you can spend it. The miner basically takes all transactions, verifies them for correctness, and puts them into a block.
If you don't wait for a confirmation: the use case would be like this:
your wallet get's notified, that a transaction has been sent to you, and you don't wait for the confirmation. You try to spend the fund of this tx for s.th. else, send it into the network, and you will remark, it does not get confirmed. This might happen, because the original sender has sent another transaction with the same origin of funds to another address (not yours). So in this case, you would "believe" to have received funds, but you actually don't have the funds. It's a trust issue. In general it is said, that 6 confirmations (after ~1 hour) make it sure, to spend the funds.
2.) You are right, it is not in your control. The miners make sure, that the network is working correctly, and security is kept to the highest level. So they provide a service, and get payed as incentive with block rewards and fees.