is this soap truly biodegradable and environmentally safe?

I am not a chemist, this product has the least chemical footprint I have researched, no FDC dyes, fragrances, or other "ingredients" which are hidden or labeled as "natural".

How is this $10 cheaper than the Dr. Bronners website?

I'm guessing at this answer, but likely the one selling it purchased a very large number from the Dr. Bronner company. As a result they obtained the product for a low price. Thus, you are getting a low price. Also, as with most products in the store, the larger the container, the more you get for the money per weight or per ounce. When I purchased it, it was the same product as sold in smaller containers in the store.

How long did this last when opened?

MONTHS!!! If you read the bottle it actually states, "dilute, dilute, dilute!" It is a powerful soap you can make as "strong" as you want...since our family uses it for about everything: bathing, washing dishes, cars, floors... (only variation is kind ie citrus, peppermint, etc) you mix it differently. We use "foamer" soap dispensers that work best/idealy making the soap come at as foam. Bathing, we use 1/4 soap 3/4 water, usually citrus. Peppermint for face cause it can be 'warm' (lol) anywhere else. Cars, a half cup per 2-3 gallons, windows just a teaspoon per gallon...but anyway you use it, a bottle that size, or jug, should last a long time...the viscosity may fool you...it is more like a water viscosity, just bc it isn't 'thick' like other commercial soaps, doesn't mean a thing....it needs to be diluted from the git-go