Now, my question is: Is this wrong or Bitcoins can really be mined? Or are the blocks the ones that are mined (solving the mathemathical problems (hash))?
Actually blocks are mined or in other words they are solved. Solving a block triggers a transactions known as Coinbase transaction. Earlier solving the block (in 2009) triggers Coinbase transaction that gave rewards of 50 bitcoin.
Block rewards are getting halves on every four year, so it become 25 in 2012, 12.5 in 2016 and next block halving will be done on 2020.
I think you should should read this book.
https://github.com/bitcoinbook/bitcoinbook