Twofold- Firstly the aim is to pass enough oxygen through the burner to cause the carbon to combust, but excess airflow will actually cool the burner and prevent ignition. Low pressure means the volume of airflow can easily be controlled, it will als be travelling slower through the burner. Secondly, if you overheat the burner to the point you melt the brazed joints (not likely) too much air pressure could blow it apart. It's easiest to see what is happening in low light conditions. As mentioned, the graphite control spindle packing will be damaged by the heat so will need replacement, and you will need to remove the nipple, pricker rack and control spindle if you try this method of burner cleaning.
When you will start the stove for the first time , it will be too late. Anyway, as any visual person, if we don't see what need to be done we are not motivated. Sorry
Through which hole in the burner should the compressed air be blown? Where the spindle normally sits or the hole where the jet should sit?
The best bet is from the bottom of the burner, where it screw into the stove. If you can roughly plug the spindle hole, even better.
It works without, but you can always find something which fits roughly, or plugs the hole, and hold it in place with wire.
Another problem: there's no inner cap with the stove I bought. I only have the outer cap. It's necessary to have an inner cap?
A good way to clean burners is the ultrasonic bath (or 3 or 4) without solvent, just a few drop of soap
Ultrasonic baths will clean off external soot but won't remove carbon deposits from inside burners unfortunately.
When I opened the box with the Optimus today I discovered a leak of kerosene. It seems to come from the jet. When I used the stove and wanted to shut it off I turned the wheel to the left. The flame died but there was still a little bit of fuel ( evaporating ) coming from the jet. I had to turn the wheel hard to the left to stop the fuel. Anyone who knows what's wrong here?
Turning to the left raises the cleaning needle, and will often also extinguish the stove in the process. The stove should be regulated and stut off by turning to the right. The cleaning needle needs to be set in the correct position to allow it all to work as intended. Optimus instructions are here.