1. What happens in the bitcoin network when two miners solve a block at the same time?
In that situation for some time 2 separate (both valid at the time) blockchains exists. Miners will start work with both versions of blockchains, depending on which reached them faster through node network. Then miners will start adding next blocks to the both blockchains and eventually one version will become longer and that version will get accepted in the network.
2. What is a stale block?
It is such a block, that was considered valid at a time of its creation: It was created during the same time as other block which was also considered valid. But this block (Stale block) “lost the race”, because other miners solved following blocks faster on the other blockchain. So this Stale block will be retrospectively erased and deemed invalid.
3. How do stale blocks occur?
Explained in 2.question
4. Why is it important to wait for more than one block to be confirmed when sending or receiving a transaction?
To be sure that your transaction is not part of the Stale-to-be block.