Or can it be viewed as a covenant (looking at it from the need of response from us) and as a testament (looking at it as God working such requirements in us)?
Yes. That is a far better way of stating the matter. Technically, using traditional terms, a covenant includes conditions and promises. The covenant of works, Do this, and live; the covenant of grace, Live, and do this. With the addition of the "testament" concept the benefits of Christ as "legacies" is clearly brought out.
Great way to explain the covenant of works (pre-fall), grace (post-fall)...
Do this and live,
Live, and do this.