No, and if the video says that then it's wrong.

Please explain to me how a bank can create base money, which is exclusively issued by the central bank.

* The bank is allowed, to lend a multiple of that $10.

False! The bank can lend only a fraction of that $10. However, if the borrower deposits that money back in the bank (i.e. makes a loan) then the bank can lend the money again, just like with normal borrowing.