You should realize that Romans is a road that must be walked step by step.
Before the verses you cite, you will find these words.
Romans 2:1-3
Therefore thou art inexcusable, O man, whosoever thou art that judgest: for wherein thou judgest another, thou condemnest thyself; for thou that judgest doest the same things. But we are sure that the judgment of God is according to truth against them which commit such things. And thinkest thou this, O man, that judgest them which do such things, and doest the same, that thou shalt escape the judgment of God?
Paul is clearly warning
all men who think they can somehow escape the judgment of God, by claiming they do not sin, or are better than others. Since all men sin....
Some men seek for immortality, and some don't even try. He compares two groups of men in the verses below, and in next two verses also. Romans 2:9, Romans 2:10
Romans 2:7 To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life:
Romans 2:8 But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath,
But here is the conclusion of the matter. There are none righteous...no not one.
Romans 2:12-13 For as many as have sinned without law shall also perish without law: and as many as have sinned in the law shall be judged by the law; 13 (For not the hearers of the law are just before God, but the doers of the law shall be justified.
Paul has many ideas in this chapter - indeed one of the most powerful chapters in Romans. He starts off speaking of judging others (v1-4), to the Judgement (v5-16) - including how the gentiles' conscience becomes a law to them (v12-15), to being a Spiritual Jew (v17-19). You could break it up even finer.
I find ideas present in the so-called conclusion to be very powerful indeed - for they show that even though God gave the Law to the Jews, he still gave all men a conscience whereby we are held accountable.
Romans 2:14-15 (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. 15 They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.)
You quoted this "conclusion" - yet you did not add an exegesis of your own. I completely agree with v13 and find it quite in line with the fact that we are to fulfill the Law:
Romans 2:13 For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous.
Furthermore, even if this were the "conclusion" of his ideas in the chapter (which it's not), it would not in anyway detract from Romans 2:6-11. It is still the case that God's judges based upon our deeds and rewards us accordingly.
You could, but not for condemnation, but as speaking of the Bema Seat where rewards and loss of rewards are passed out. Nothing there about our earning or being rewarded with salvation.
Oh, I can think of a number passages that speak of rewards and condemnation. The scriptures are very consistent (including the OT) at declaring that if you do what is good and right, you will live. If you pursue evil then you will be condemned and die. And the passages which only explicitly emphasize the reward also clearly infer the opposite as well.
Deutoronomy 30 (read the entire chapter, but especially the last half).
The parable of the Sheep & Goats (Matthew 25:31-46)
Matthew 7:21-23 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven. 22 Many will say to me on that day, ‘Lord, Lord, did we not prophesy in your name and in your name drive out demons and in your name perform many miracles?’ 23 Then I will tell them plainly, ‘I never knew you. Away from me, you evildoers!’
Hebrews 10:36 You need to persevere so that when you have done the will of God, you will receive what he has promised.
James 1:12 Blessed is the one who perseveres under trial because, having stood the test, that person will receive the crown of life that the Lord has promised to those who love him.
1 Cor 9:24-27 Do you not know that in a race all the runners run, but only one gets the prize? Run in such a way as to get the prize. 25 Everyone who competes in the games goes into strict training. They do it to get a crown that will not last, but we do it to get a crown that will last forever. 26 Therefore I do not run like someone running aimlessly; I do not fight like a boxer beating the air. 27 No, I strike a blow to my body and make it my slave so that after I have preached to others, I myself will not be disqualified for the prize.
I could go on. Many of these speak of both reward and condemnation. Some only explicitly speak of the reward, but also very clearly imply the condemnation (for if you do not get life, what is waiting for you but death?) Some from Jesus, some from Paul, Some from James, etc. The scriptures a extremely consistent on this point.
Yes, I do agree with the other three, unless you mean something other than what you have written plainly there. Those are saved who hear the Gospel of Grace...the preaching of the Cross. God shows no "favoritism"...His Grace is offered to all men. It is man, himself, who chooses to reject God. Not the other way around.
That is good. However, we know that "choosing" goes beyond belief (if indeed belief even be counted as a decision as such). For, "You believe that there is one God. Good! Even the demons believe that—and shudder." James 2:19.
So what, more specifically, would you say one must do to choose God and be saved?
Of course, Paul among others tells us: we are judged by our deeds. We must do what is good and right.