1 What happens in the bitcoin network when two miners solve a block at the same time?
When two miners solve a block at the same time through a cryptographic puzzle and the hash in their block reaches below the target number, they both will be able to propagate their block through the network. Two versions of truth will be running concurrently and both versions will be valid regardless of the different transactions the miners hold. This will result in a split in the blockchain. When a third miner chooses to append their new block into one of the two blocks, that blockchain will be longer than the other competing blockchain. The network will in effect accept the Proof of Work of the longer blockchain while removing the transactions of smaller block back to the mempool.
2 What is a stale block?
A stale block is a block that has been removed.
3 How do stale blocks occur?
Stale blocks occur when two blocks are propagated through the blockchain at the same time and one is dropped. The one that is removed has a shorter Proof of Work in the blockchain than its competing block and did not reach 6 confirmations.
4 Why is it important to wait for more than one block to be confirmed when sending or receiving a transaction?
It is important to wait for more than one block to be confirmed when sending or receiving a transaction in case your blockchain gets dropped. By waiting for 6 confirmations you would minimise issues relating to a stale block.