Question #1: What is "walking according to the Spirit"?

The language, at least in my translation, suggests that walking according to the spirit can’t be an unconscious change that happens without your knowledge or your trying. This is because of the words “walk” and “set their minds on” (that said, the NIV leaves it way more ambiguous, saying “have their minds set on” and “controlled by the sinful nature”). So then, it’s something conscious, that we choose to do when we receive the Spirit. I am guessing that the free gift of grace is that the Spirit is in us, in spite of our sin, guiding us as to His purposes and forgiving us when we fail to do what we should and transforming our hearts to want what he wants.

This would be, in my plant metaphor, like the branch being grafted on. It’s an opportunity that we don’t do anything to deserve and can’t do anything to help besides accept the gift. As far as that's concerned, it's a bit of a mysterious process that we can't do anything to help along. But after the graft comes the slow process of the branch rejecting its old nature and accepting the new. The gardener grafts you on, but your actions and decisions determine whether or not the graft will take. Every part of you needs to be transformed, and your actions and choices do allow the transformation. You "set your mind on" the things of the Spirit.