I am still working on the other verses, but refuting your understanding of these verses in Romans were so easy, I picked them first...
Verse 1
“What shall we say then? Are we to continue in sin that grace might increase?”
Paul has just spent the previous 5 chapters proving that ALL men are guilty of sin (chapter 1); That they cannot use the Law to compare themselves against one another, because the Law is what proves ALL men are guilty of sin (chapter 2); That righteousness (freedom from sin) comes by faith alone in Jesus Christ, and not be the works of the Law (chapter 3); That God chose Abraham as the father of all who believe God will give us this righteousness as a result of Christ's sacrifice for sin so that we are now justified by faith, and not by works (chapter 4); and even though all men are sinners because of the disobedience of one man (Adam), yet all men may receive life because of the obedience of only One Man (Jesus).
Romans 5 concludes:
"And the Law came in that the transgression might increase; but where sin increased, grace abounded all the more, that, as sin reigned in death, even so grace might reign through righteousness to eternal life through Jesus Christ our Lord."
Sin reigned in death, Knight. Are you still dead?
Therefore, the obvious question in Romans 6:1
"What shall we say then? Are we to continue in sin that grace might increase?"
This is a rhetorical question, because Paul already knows the answer. But, it is an obvious question based on his conclusion in chapter 5. (paraphrased) "Why not keep sinning so that the grace of God (which is greater) will increase all the more?"
Paul makes the answer abundantly clear:
Verse 2
"May it never be! How shall we who died to sin still live in it? "
Paul is emphatic! We have died to sin, and therefore it is impossible to live in sin! Not some legalistic recommendation that you shouldn't be sinning, but a clear statement of the impossibility of the event.
Paul goes on to explain why it is impossible for you to live in sin.
Verse 3
"Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death?"
Anyone who has come to Christ by faith, has been baptized into His body, and has shared in His death (and resurrection).
Verse 4
"Therefore we have been buried with Him through baptism into death, in order that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life."
This "newness of life" is not a changed life, but an exchanged life. We give Him our life, and He gives us His! We are a new creation. We are not under the law of sin and death, but the law of the Spirit of life in Christ.
Verse 5
"For if we have become united with Him in the likeness of His death, certainly we shall be also in the likeness of His resurrection"
When Jesus died to sin, so did we, and the life that Jesus has is the very life of God, and so is ours!
Verse 6
"knowing this, that our old self was crucified with Him, that our body of sin might be done away with, that we should no longer be slaves to sin;"
Your "old self" is who you were in Adam, in sin, and dead (separated) from God. Jesus crucified our old self with Him, to separate us from the body of sin, so that we are no longer it's slave.
Verse 7
"for he who has died is freed from sin."
Have you died with Christ? If so, then you ARE free from sin.
“For you have died and your life is hidden with Christ in God” Colossians 3:3
“It is a trustworthy statement: For if we died with Him, we shall also live with Him”
2 Timothy 2:11
Verses 8-9
"Now if we have died with Christ, we believe that we shall also live with Him, knowing that Christ, having been raised from the dead, is never to die again; death no longer is master over Him."
Jesus died to sin, and those of us who died with Christ are also dead to sin; However, we have also been made alive in Him, and death is no longer master over us.
Verses 10-11
"For the death that He died, He died to sin, once for all; but the life that He lives, He lives to God. Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus."
Why must we consider this? Because we need to renew our minds with that which is true, as Paul has already proved we are indeed dead to sin, but alive to God in Christ!
Verses 12-13
"Therefore do not let sin reign in your mortal body that you should obey its lusts, and do not go on presenting the members of your body to sin as instruments of unrighteousness; but present yourselves to God as those alive from the dead, and your members as instruments of righteousness to God."
So now, because you are "free from sin", it is ludicrous for you to allow sin to reign in your body by obeying it, rather than obeying righteousness by faith in Christ. Are you going to go back and undo all that Paul just explained from chapter 1 until now, and obey the Law for righteousness and once again declare yourself a sinner, thus obeying sin? Which is it? Are you going to go back and present the members of your body to a system that proves you a sinner, or are you going to present yourself to God as what you are... an instrument of righteousness? Are you in sin or in Christ? Are you dead or alive?
Verse 14
"For sin shall not be master over you, for you are not under law, but under grace"
Sin has lost it's power in your life, not because you are obeying the Law, but because you have died to it through Christ's sacrifice, and you are now alive in the Spirit, by grace through righteousness.
Verse 15
“What then? Shall we sin because we are not under law but under grace? May it never be!”
Again, Paul asks a rhetorical question, and once again he already knows the answer...
Verse 16
"Do you not know that when you present yourselves to someone as slaves for obedience, you are slaves of the one whom you obey, either of sin resulting in death, or of obedience resulting in righteousness?"
If you are going to live according to the Law, then you will be proved a sinner, and you will be a slave to sin, and the result is death. However, you can obey the gospel of faith alone in Christ, which results in righteousness, and be its slave.
Jesus answered them, "Truly, truly, I say to you, everyone who commits sin is the slave of sin.
John 8:34
Verses 17-18
"But thanks be to God that though you were slaves of sin, you became obedient from the heart to that form of teaching to which you were committed, and having been freed from sin, you became slaves of righteousness."
What is the form of teaching? It is the gospel!! The gospel of Jesus Christ sets you free from sin, and makes you a slave of righteousness. You can no longer become a slave of sin, if you are in Christ Jesus.
Verse 19
"I am speaking in human terms because of the weakness of your flesh. For just as you presented your members as slaves to impurity and to lawlessness, resulting in further lawlessness, so now present your members as slaves to righteousness, resulting in sanctification."
Oh how the legalists love to pervert this verse perhaps it is their weak flesh, but Paul is trying to make a point about who you are going to serve; either the Law which results in proving your sin, or righteousness through faith in Christ which results in your sanctification (being set apart from death).
Here is where so many get confused, and why so many go astray from the truth. Presenting your members is not behavior modification through obedience to the Law, because if it is then Paul just contradicted his entire arguments from chapter 1 until now. No, Paul is showing us that we need to present our members to righteousness which comes by faith, rather than trying to gain God's favor with them through keeping the Law. "Walking in the flesh" is not "sinning", it is believing that God approves of you through the deeds of the flesh.
Verse 20
"For when you were slaves of sin, you were free in regard to righteousness."
When we were in Adam... dead, and separated from the life of God, there was never a possibility of ever doing anything right. We were free from all righteousness.
Verse 21
"Therefore what benefit were you then deriving from the things of which you are now ashamed? For the outcome of those things is death."
All your works, deeds, etc. were pointless, and now that you are in Christ you can clearly see that your own efforts fell short of pleasing God, and it shames you to think that you could actually gain his favor through the Law. The only thing you could produce in Adam, was death.
Verse 22
"But now having been freed from sin and enslaved to God, you derive your benefit, resulting in sanctification, and the outcome, eternal life."
Having concluded that in you there dwells no good thing, and that apart from God's righteousness you are without hope, you have come to Christ by faith, and have been set free from sin, where there is true benefit and true life!
Verse 23
"For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord. "
Which will you choose? To live under a system that can only produce death, or to accept God's free gift of life?