The default screen behavior is normal as it dims the screen when in battery to save power so battery lasts longer between charges but is fully customizable by user under System -> Preference.
Whether leave machine plugged is been asked since the dawn of times so u will get more than a few different replies.
My Air is 6 years old, battery at 938 charge cycles, 79% health. I keep in plugged in when in use and leave it like that until am done for the day or it's gonna be unused for a long while (hours) and it's already fully charged, then I pull the plug. I use mine every day and discharge the battery between 10-50%. What the first numbers signify, it's telling me a battery change is due soon. Expectancy of battery lifetime charge cycles is ~1,000, and when it drop to 70% health, the end is near, but is really depends how many hours you need it on battery. If I have a need to keep it on battery longer than what I need it today, I probably had replaced it already for max endurance. But for sure, don't obsess about it, just don't leave it in a hot car if that's not already obvious.
