It's the predicative instrumental case. Let's take the phrase "Они сделали жизнь интересной" (= They made life interesting ) as an example. In this phrase, "они сделали интересной" (they made interesting) is a predicative expression and "жизнь" (life) is a direct object (in the accusative case). Since the adjective is a part of a predicative expression and the noun is an object (i.e. they are different parts of the sentence) they shouldn't agree in case. The adjective or participle as a part of the predicative expression takes the instrumental case. It doesn't really have any semantic meaning, you just need to remember it.

Because "сделали" asks for the instumental case. (сделали кем, чем). Их жизнь такая, какою они ее сделали. But both variants are correct as for me. Simply "какой" and "какою" both are the instrumental case of "какая". Two variants.