Yes. There was no agreement in place during WWII that protected occupants parachuting from an stricken aircraft (paratroopers or otherwise). The 1923 Hague Rules of Air Warfare might have, but they were never went beyond draft stage.
The 1949 Geneva Convention, Protocol I, Article 42 provides protection for aircrew bailing out of disabled aircraft, but paragraph 3 specifically excludes paratroopers from that article.
Given that the thinking just after the war permitted firing on paratroopers, regardless of the status of the aircraft, its clear it would not have been considered a war crime. The reason, of course, is that the paratrooper is still considered a combatant. His mission is to reach the ground and fight.
Edit: As u/RonPossible pointed out, the Geneva convention article about paratroopers being explicitly excluded from protection was not in effect until after WW2. Which means, you are just a soldier and normal ROE applies.
Yes. You are an armed, uniformed soldier, who is participating in a coordinated attack.
ROE, allow enemy soldiers to shoot at you. Regardless, they did.
Not sure how many sources are needed here. But the ROE are available online, from multiple sources, and combat footage and testimony shows that paratroopers were targeted.
I mean, if you are a soldier, why wouldn't you shoot enemy paratroops? Besides them being hard to hit?