For flights cheapest usually involve long layovers on less world class airlines.
If he's flexible and doesn't mind too much about the service then just use Skyscanner to find cheapest route options.
Often it is cheaper to fly from a European hub rather than from the UK. Often flying into Germany on a budget airline and then taking a long haul flight from there seems to work out more cheaply.
I always book direct with the airline. You have a direct contract with them, and nearly always the cheap prices other sites offer are just to lure you in and then they put them up after the initial booking enquiry.
We always fly Singapore airlines now as I've never had a bad flight. But have flown Thai (hated it), Malaysia (was okay), Swiss (was okay) and Emirates (was okay) previously. My friend has just flown Etihad had said it was awful.
If he has the extra time, I would suggest he takes a few days for the layover and explore somewhere else on the way( or way back). That may help him narrow down airlines to those that fly in and out of that location. You could look at Emirates, Qatar, or Etihad etc for the Middle East; Cathay, BA, etc for Hong Kong; Singapore, Qantas, BA, etc. for Singapore. Or other carriers for other places.
In terms of treats, I missed UK crisps, chocolates and sweets. But you can get most of these in the international section in Coles now. I would just send her some money towards a day trip.
Has she been out to Mornington? There are hot springs which is a fun day. Or a little further there are penguins at Phillip island.