What happens to transactions included in extinct or invalid blocks? I have read that a block contains several transactions. 

An attacker can forge fake a block.

The blockchain is safe because the system will choose and keep the longest chain.

So the fake block will be lost.

This is great but what happens if my transaction was included in the fake block?
Let's suppose I am buying a car. Should I wait for 6 confirmations to be sure? That would mean that I have to wait one hour!
what happens if my transaction is in the fake block?


It is also in the memory pool (mempool) of pending transactions at other nodes run by more honest people and will be included in a new and valid block in the normal way.


  Let’s suppose I am buying a Tesla car. Should I wait 6 blocks to be generated to be sure? But I have to wait 1 hour!


Yes.

There are faster payment methods for Bitcoin - e.g. Lightning Network (LN) and arguably perhaps escrow services. But they have their own trust model and characteristics you need to understand when using them.