Paul begins this chapter with a comparison of two ways of life: physical and spiritual. Living "in the flesh" means that there's no way to go but down. All flesh decays no matter how much Botox gets injected into it. And living "in the spirit" still must take place in our physical existence, so we have to keep our personhood in such a way that it is guided from above into a life of God's freedom. Paul speaks of a "law" of the spirit that liberates from the law of sin and death. We're made free before we fully realize it (assuming that we ever do fully realize it). Actually, verses 1-4 make a pretty complete summary gospel statement all by themselves.
In these verses, we read of a distinctive relationship that is possible with God. Bondage and fear are replaced by the joy of being a child of God and a joint heir with Christ in a large family. We are assured that when all we can do is express "sighs too deep for words" the Spirit will articulate our prayers for us.
There is also a very odd statement about all creation longing for and sharing in the redemption of man. Somehow animals and nature are a part of redemption? That's curious.
This often quoted verse expresses a vague Stoic optimism. "All things work together for good" doesn't mean that everything that happens is good. It certainly doesn't mean that everything that happens is God's Will. God doesn't cause evil or sin, that is, "bad things". There is nothing in life to encourage the easy optimism that everything will work out to the satisfaction of good people. In Herschel Hobbs' commentary on the book of Romans, he says that as this verse reads in the King James Version it expresses not faith, but fatalism -- somehow, someway, things will turn out all right. Hobbs says that some translations of the original texts put "God" as the subject, that is, God works through all things with his eternal redemptive purpose.
I get chills every time I read this passage regarding the invincible love of God. In a series of questions and answers Paul comes to a soaring climax of his first eight chapters in concluding that , "I am persuaded that neither death nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord."