That is not true. Germany has robust self defence legislation, thanks to Kaiser Billy.
In self defence, any means available are legal. Self defence does not only cover your life or health, but your property as well.
Totally wrong.
Any means are legal, that would even include a illegal owned weapon.
That is nonsense. Any means legal for defence means killing included, if the attack persists. If you have made it impossible for the attacker to continue the attack, either the attacker is physical no longer able to attack or has decided to stop and retreat then the legal excuse of self defence no longer covers any further activities against the former attacker.
As long as the attacker is a threat, self defence is legal in Germany. You can stand your ground, your right has not to give way to crime, but you are not allowed to seek confrontation.
You are allowed to help someone else in a self defence situation. That is what the under cover cop did.
The police man fired the warning shoot for juridical cover. A warning is not obligatory, like if any hesitation would lead to (more) harm.
He did that to give them a chance to stop, so in case he had to shoot against the man, he could claim it was needed (persistent attack) deadly force in defence of the other man.
German police guns have life rounds. German police men are not as trigger happy as in the USA, but they don't need to ask their superiors for permission for deadly fire either.
Actually shooting to kill is illegal in Germany, but it is legal to shoot to stop an attack. If the perpetrator is dead as a result, that is excused by the law. Just wounding as a result would be legal as well, but dead men don't talk (nor do they draw hidden weapons).
It would be illegal to shoot a fleeing criminal, even if he carries away your possessions, because the attack is over (even if he illegally possess your stuff). You can try to catch him to get your stuff back, if he resists and attacks you, you are back in self defence (not advisable because of physical and legal risk).
Nearly nobody is allowed to carry a gun in Germany, beside of the police and the kikes.
So self defence with a gun is purely academic outside of the homes of legal gun owners, who are not allowed to carry. Not even cops are allowed to carry outside of duty. Even at home, the few legal gun owner are obligated to store the guns unloaded and locked away. Nearly any case of gun home defence is a case of violation of German gun law.