MacBook Air shows battery as power source when plugged in

Don't worry. It will use the wall outlet if that offers enough power which it should using the original AC adaptor.

What if the power is going from 100% down to 99.6%, then back up to 100% constantly?

That was until about a decade ago or so. Modern laptops even don't charge your battery if it is eg. at 98% for reducing unnecessary cycles. Don't bother about your battery in your computer.

If you want to care for your battery, just remember every cycle shortens battery life, no matter if 10 minutes on battery or completely emptied it. The battery has also some natural aging, so it will die after some years even if you never touch it.

I still don't understand your question.

You want to plug it in but not charge the battery? Why?

My vague understanding about batteries speaking with hardware repair shops, etc. is that it's no longer truly worth worrying about. You charge when you can, you use the battery when you must. While plugged in, the battery charges until full and then stops charging. Presumably, at that point, it's using the power cord and not the battery.

The other thing that I seem to recall is that it's all about the charge cycles. You want to keep that number down. So, if you work from home one day, it would be better to leave it plugged in all day because that would only be one cycle (assuming you plugged it in first thing in the morning). If you plugged it in until it was charged, then unplugged it and used it until it was low on battery, then repeated, that would be 2, 3, or 4 charges during the day depending on how you use the computer.

So, what I've heard from people much more knowledgeable than I, is that the potential gains you might experience doing "the right thing" are not worth the effort required to realize those gains.