SybilVimes posted:

Aircraft don't really photograph well with the 3/4 view, so the first shot would probably have been better done almost directly head-on and moved back the 50' or so for the second shot's position .

For aircraft with a prop, you want to be on shutter priority, in a good day you're going to have plenty of aperture available even down to the low fractions of a second.

At that focal length you should have been able to get down to 1/60th (or 1/80 - 1/100 and some safety room) without running into a major problem with vibration/shake. That would have given you better prop disks, a smaller aperture, and thus a wider DOF to get more of the plane in critical focus. Also, the sky is blown, which could probably be solved in editing if the camera saves raw files. Otherwise, maybe a -0.3 EV compensation would have kept the sky (or better use of controlling the exposure/metering, if the camera allows it, but it probably doesn't).

The sun appears to be direct overhead, which is always going to give you pretty lovely light no matter what, but you probably had no control over that.

As for heat shimmer, not much you can do apart from being closer, sometimes it can add to a picture if everything else is perfect.

Editing wise, the major thing with that heat haze is that you don't have too good contrast natively, so you'd want to push the contrast as best as you can without it getting too obnoxious. If the sky wasn't blown, you should have had blue sky in that direction (if I'm judging from the other pics right, the clouds were mostly behind you), that would have improved the contrast somewhat.

The rule of thumb for 'safe' shutter times without vibration being a problem; is 1/focal-length, since your focal length is ~50mm, that should allow you plenty of options on capturing the prop disk, and while taxing the plane isn't going to be moving fast enough for motion blur to be an issue.