Can I put a car stop onto block paving?

No it would not be strong enough would suggest removing the block paving in that area and then set the car stop in concrete then put the block paving back around it.

Yes you can have installed a post in a block paved driveway. To protect the wall & car regards J&M GROUNDWORKS

As one comment mentioned, it will not be strong enough unless you remove the blocks and laying course and pour in some concrete on the sub base so you could drill into it, so it will hold. The reason being is because block paving is unbonded, meaning it is just lay on compacted sharp sand, so if you drilled the stop into the block, then if it needed to do its stop and stop a car, then it could potentially pull the block up when under resistance. So yes it is possible, but it must be done properly.

As long as the stopper is bolted in the middle of blocks and only used as a marker this would be fine

I would personally concrete this in before laying the blocks and then block pave around it