Excellent questions, @Mshumack - I see you’re delving into what is often considered the meat of the word - very good!
Romans chapters 5-8 are about the ongoing process of sanctification that follows our justification (which was covered in the first four chapters).
To clarify, justification can be thought of as the precise moment of conversion when the repentant sinner believes the gospel and is saved from sin’s penalty in hell. Sanctification is the lifelong process of spiritual growth as the believer is progressively saved from sin’s power over his daily life.
Chapter 5 begins by listing all of the blessings of justification (essentially describing the sanctification process). And it ends by explaining the basis of our justification (grace).
And this brings us to the three chapters you’ve asked about.
When you start telling people that salvation is through faith in the free grace of God apart from any works on the part of the believer to earn it, some will object that this sounds like a license to sin. If sin makes grace abound (Romans 5:20), then why not sin with abandon so grace can abound with abandon (Romans 6:1)? Why not sin all we want if we’re not under law, but under grace (6:15)?
But Paul explains that anyone whose inner nature actually wants to sin has obviously not been reborn. (Now, the flesh will want to sin until the day it dies - but sin grieves the Spirit in a child of God.) He explains that the moment you were justified, the old person who had lived inside of you before was crucified with Christ (verse 6) - dead and buried - never coming back.
But wait - you’re still alive! So who’s that inside you now? Looking out through your eyes? Sitting at the controls of your life?
As the old person you used to be died, the Spirit of Christ was simultaneously raised up within you (6:11). That inner death, burial and resurrection means that you’re not the same person you were before. That Spiritual baptism on the inside that only God could see (6:4) now gives you a new mind, a new heart, a new will to live for God that the old “you” never could have had (6:2).
But the death of the sinner and the resurrection of the saint on the inside has not yet happened on the outside. Someday it will (8:23), but in the meantime, every Christian has the soul of a saint inside the body of a sinner - the nature of God inside and the nature of Adam outside (7:21-25). And this causes the believer a lifelong conflict between the sinful flesh urging your will to gratify its various carnal lusts, and your righteous Spirit urging your will to deny the flesh and use your body to honor God (6:11-13 and 7:15-20).
For example, your Spirit wants to be at peace, but someone makes an insulting comment, and your flesh churns out adrenaline that makes you want to swing a fist - and your Spirit has to say, “No flesh! Down flesh! Bad, bad flesh!”
Your Spirit wants to be pure, but some bikini babe goes bouncing by, and your flesh churns out hormones that disturb your thoughts - and your Spirit has to say, "Bad flesh! Down flesh! No, no flesh!
In these chapters, Paul uses the phrase in the flesh to describe unbelievers. They are under the power of the flesh because everything the flesh wants to do, the “old man” (6:6) sitting at the controls of their body is fully on board with. He is spiritually dead and so he has no spiritual motive to restrain anything the flesh demands (8:8). So in the flesh describes unbelievers, not believers in these chapters.
And by contrast, Paul uses the phrase in the Spirit to decribe believers (8:4). Everyone born of the Spirit is in the Spirit (8:9). How wobbly you walk is not the issue here. If you walk for God at all you’re doing something no person in the flesh ever could (8:7).
But all of our conflict between the saint inside and the sinner outside is temporary. What has already happened in the Spirit will one day happen to the body as well, and the outer man will finally catch up with the inner man in the resurrection (8:18-23). And then we’ll be whole and holy!
And in the meantime, God says no condemnation upon (8:1) and no separation from (8:39) His followers, because once your soul has been transformed by grace, your ultimate Christlikeness in glory is a foregone conclusion (8:29).
I hope this, along with your others responses, will help you make better sense of these epic chapters!