Excellent work so far, a couple of minor points:

His name was Herbert Davies and he was with the 10th squadron.

In the RAF (and other Commonwealth air forces) it’s always 10 Squadron (“Ten Squadron”) never ‘tenth’, as that’s an American designation.

I think he was ranked a flight leutenant

You mean ‘lieutenant’, written the same but pronounced differently in different forces. (Apart from pedantry, it’s worth getting these things right as they help with searching – online or elsewhere. Hope that helps.)

… my mum seems to think he had been an ‘acting captain’ though a battle commission or something.

Probably simply that he was the pilot and therefore the ‘aircraft captain’ or ‘the skipper’. In both cases it’s not a rank, but a job (or role).

There were ‘field promotions’ and the like in the Army, but not, as far as I’m aware, ever in the RAF or companion air forces.

Through the years he gained the DFC whilst operating over Europe before VE day and after that went on to fly POWs home to Australia, …

That’s very interesting, and I’d like to hear more about that. As far as I know only one Halifax was used to fly families home from Europe, and that was a private endeavour organised by the aircraft designer G. N. Wickner and crew, but your chap’s name doesn’t appear. ( http://www.pprune.org/aviation-history-nostalgia/236813-halifax-lancaster-used-emigrate-australia-after-war.html ) That’s assuming he’d be flying the type he’d flown during the war. What’s far more likely is that the postwar work was with an airline, rather than RAF or RAAF. Anything you find would perhaps open up into more info – not enough as yet, sadly.