4.07 is rubbish

[Feuerfalke]

JFYI: Patch 4.08 is the latest patch.

The BI-6 keeps flying when it's out of fuel, because the rocket-engine on the back runs out of fuel before the other engines do. So you probably get the out-of-fuel-warning from the rocket engine, while the main engines are fed with a different fuel.

Last not least: No one forces you to fly those 1946 planes. They are not realistic, because a large portion of them never existed or at least never flew. But as you already stated, there are a lot of missions for these planes, which should also give you the hind, that these planes are flown and loved by others.