https://blockchain.info/block/000000000000000005171a134d8aa60ff465514266a5422477fe1489bd00dc2e how is it possible to mine such block?
Miners can choose what transactions they want to include. If they don't want to include any transactions other than the one that pays them their 25 BTC, then that's their choice.
Correct. But if miners decide to make Bitcoin useless that way, they're also hurting their own profit. That is why these 1-transaction-blocks are quite rare fortunately.
No it actually helps their profit to include very few transactions, since they get less orphaned blocks this way. For example, Discus Fish pool used to only include no more than 42kb worth of transactions in every block they mine. Then the Bitcoin community threatened with action, and Discus fish bowed to the community pressure, and now includes more transactions.
