Soaking them, I have been told, also removes some of the less healthy elements within them.

Selling unsoaked nuts is IMO comparable to selling dry rice. I feel food packaging should do more to inform you.

I usually soak them overnight. I will soak then around 10-11 PM and by morning they are soft and tastes a lot better.

Do you toss the water out or does it have any benefit?

The water doesn't have much if any nutritional benefit, but if you like the flavor, you can add it to other things.

Depending, it may be good in smoothies or to steep tea in, to add to rice, oats, or quinoa, or as part of the stock liquid when cooking.