validation of a block with false transactions When a miner can find a number to create a hash with enough zeros, the other miners can verify his work by testing that number and seeing if everything is correct. But how do they verify that the transactions in the block are not false? How do they see that the amounts are properly authorized? An attacker could create a transaction in which Alice sends him 5 BTC, without Alice knowing about it. Is it possible?
The block validation process involves checking that all the individual transactions in it are all valid according to the consensus rules which are set in the Bitcoin Core C++ implementation.

Block validation is done by Bitcoin full nodes and one would assume by all miners. If a block is not valid then it will be rejected and any miner who attempted to insert an invalid transaction would have wasted all the time and effort to generate the block hash.