This question has come up here before and per the previous answers, the purpose of clarifying it is to make it last longer. But also it doesn't brown as fast as regular butter.

Ghee is clarified butter, meaning the removal of all milkfat. This means it has the shelf life of olive oil, about 1+ years, no need to refrigerate.

In the fridge for quite some time - like a year or so - provided you have only used a super-clean spoon to dip in a out of the jar. if you see any fuzzy bits around the edges I'd toss it. if it's been in a cabinet, it may have gone rancid - so you'd have to taste/smell to be sure.

I've kept a jar in the fridge for about 9 months and didn't suffer any ill effects toward the end of its useful life.

It lasts for a long time in the fridge, exactly how long, couldn't say, but even if stored outside of fridge, it'll last if in an airtight container.