1.In the transaction, when the receiver receives Bitcoin and how the receiver knows that he/she receives Bitcoin
Transaction are submitted to the Bitcoin network and are then included in the a block in the blockchain by miners. The first block that contains the transaction results in the transaction having 1 confirmation. Each subsequent block mined after than is another transaction.
The receiver of bitcoins in a transaction (and everyone else) will know about it once the first confirmation is there. For reasons that are probably beyond the scope here, it is recommended to wait for 6 confirmations before considering the transaction "final".
If the person wanted to, he could even probe the network and know once the (unconfirmed) transaction hit.
2. What will happen if there are no Minors in the network.
Bitcoin will die.