Re the Coriolis thing - I'm not sure if this will make it any clearer, but after much scratching of the head (it was a 2-Columbo problem).......
There is no Coriolis at the Equator within about 20 degrees either side, but elsewhere, when going East, you are moving with the Earth, so your velocity is greater (similar to having a tailwind). Of course, going the other way, you will be going against the Earth's rotation, and will be slower.
You are accelerating, in that the nose is going downwards to maintain your altitude, so there is an element of centrifugal force involved, changing its value with the changes in acceleration mentioned above - enough to cause a deflection towards the Equator when moving faster than the Earth, i.e. West to East, or towards the Pole when travelling slower than the earth, or East To West. Either way, the deflection is to the right.
The centrifugal force is balance by gravity when you are at rest, but once you start moving, it changes.
Back to Columbo...