Some help at least.

On Q1, it's your passport that matters, UK passport has no visa payment (free 30 day stamp on arrival).

On other points, flying the 2 big carriers (Etihad and Emirates) can often mean they'll arrange your visa for you. However, the Canadian "situation" is new so not sure what to advise except call the carriers and ask if they'll throw in a visa with the flight.

In terms of overall itinerary, would say spend 4 days in Oman, 4-5 in UAE and 1-2 in Qatar.