If I possess a humanoid using Magic Jar and stay next to my original body, then someone moves the jar more than 100 feet away from me and destroys it, will the possessed creature die and will I be safely put back in my own body?
In your scenario, you will be safely returned to your own body while the possessed creature will die.
Let's break down what happens to each creature when the container is destroyed while being more than 100 feet away from both creatures.
The original caster
If the container is destroyed or the spell ends, your soul immediately returns to your body. If your body is more than 100 feet away from you or if your body is dead when you attempt to return to it, you die.
So as long as you (occupying the possessed body) stay next to your original body, your soul will return to it upon container destruction, regardless of the distance to the container.
The possessed creature
If another creature’s soul is in the container when it is destroyed, the creature’s soul returns to its body if the body is alive and within 100 feet. Otherwise, that creature dies.
Given that the container is more than 100 feet away from the possessed body (which you now occupy) when it's destroyed, the possessed creature will die.