Starting from point 3
As far as I can work out, there'd no benefit to having a centaur pilot as opposed to a human one. Their physical strength and speed are no advantage to them, but rather are detriments.
But... then again
Though... maybe you could extrapolate some advantage in that centaurs/horses have larger lungs and bigger hearts (and possibly two hearts), and so might handle G forces and high altitudes better?
They would have an easier time staying warmer, being a larger creature with some fur. So, thinner pilot jacket, less discomfort and clothing to handle the cold. That would only be a minor benefit.
Hunters had good records as pilots, with many of the flying aces having been hunters. So the culture of hunting and marksmanship associated with centaurs might make them better shots and fighters on average... if their plane is still manoeuvrable enough that they had a fighting chance, that is.
Regardless of their effectiveness, I imagine national pride would lead to experimental centaur fighters, who may be used in a war. If their results were good, they might make more.
Let's move onto how the plane characteristics might be effected.
Size and weight
A centaur is long, tall, and heavy. Maybe they can lean forward, the equivalent of a horse reaching its neck forward, to reduce their height... but that does increase the length issue.
This could necessitate a larger plane. Though if you removed the copilot, they might fit into the plane by lying down, and it wouldn't need to be much bigger? That could be helpful, so that it's a fighter plane instead of a small bomber.
It may not be practical to give centaurs parachutes, since quickly exiting the craft and the expense of producing such a large parachute may be prohibitive. On the bright side, parachutes weren't that common through WW1. Planes were flying low enough that it was a dubious proposition for a fighter pilot.
I do wonder if you could produce parachutes for centaurs at that point in history.
Those things together, the plane might have a very large passenger compartment, filling the position of the pilot and copilot. Anything important in the plane between those points will have to be moved elsewhere, which may mean a larger plane. If the added weight of a centaur (anything from 900lbs to 2,000lbs) was an issue, they might need a more powerful engine, which could make the plane a fuel guzzler.
If those things are true, then a larger, heavier plane with more powerful engines could make for a unique fighter design. You might even exaggerate it by adding additional armour or engines? Potentially, it could be that centaurs don't build pure fighters, but instead building something more like a fighter-bomber.
If you can make an air-doctrine which can emphasize the strengths of greater armour, power, and maybe firepower, then this could help subvert the weaknesses of the centaur. They probably have a history of Mongol-style tactics, so they might be skilled at bombing runs or even feigned retreats.
With more powerful engines, you may be able to outrun enemy fighters, although mobility is likely not great, compared to the Steppe ponies of the Mongols. You may have to compare them more to the heavy horse charge of knights, where in this case instead of lances they would use M2 Browning .50 Calibre machine guns, with a heavy enough plane and pilot that you DON'T want to be playing chicken when they dive in your direction.
Can you build it?
I can only guess at this, as I lack the data to approximate how difficult an extra half ton of weight is for WW1 planes. But, towards the end of the Great war... I think it's possible. By WW2, you certainly have fighter-bombers, and they were being developed at the end of the war.