I've re-done the layout so that it displays legibly on my iPad, and have incorporated most of your suggestions, including rough hacks at seasonality, daily temperature range, and violence of weather. More things have been normalised to Earth, and I have added at least space for most of the things you asked for.
How does it look?
<edited to add>
Here's a planet with a moon to show the workings of the "celestial objects" box:
Tian Longshan.
Here's a tide-locked one:
Hijra. In this case the "daily temperature variation" displays the amount by which the day face is warmer than the listed average.
And here's one in spin:orbit resonance:
Toutatis.