Question that was never answered for me about Peter

Exactly, it's one of the many things that is left deliberately ambiguous.

Although in their research, P&P did find a record of a tail gunner who had been blown out of a plane at many thousands of feet up who fell without a parachute (no room for a parachute in a bomber's tail gunner's turret) but he survived. Although he fell through trees onto a snow covered hill. But it gave them the idea for Peter

Steve

When Peter woke up on the beach his vest looked like a life preserver. May be that's how he survived he floated on the water.

He wasn't meant to survive though, the films supernatural answer is that the grim reaper couldn't see him in the fog.

So it depends on if you see it as all an hullucination or view it as a real experience. If it's all in his mind, caused by the brain thing, then it is pretty impossible that he would survive.

If everything we see in the film is real, and not a hallucination caused by his brain tumor, then the only thing that seems possible is that by the time he jumped the plane was very low, and not going very fast. There might have been a slim possibility of him surviving the impact with the water. I don't know what the water temperature in the Channel is in May, but if he was floating out there for more than an hour or so, it's probably equally remarkable that he didn't die of hypothermia.