Romans is one of the four letters of Paul known as the Hauptbriefe, which are universally accepted as authentic. It is typically dated c. 57 CE.
Charles D. Myers, Jr., writes on the place of Romans in the genuine correspondence of Paul (The Anchor Bible Dictionary, v. 5, p. 817):
A relative chronology of the Pauline Epistles can be constructed by means of references in Paul’s genuine epistles to the Jerusalem collection. This collection was inaugurated at the apostolic council described in Galatians 2, when Paul agrees to “remember the poor” (Gal 2:10). The collection was introduced to the Corinthians in 1 Cor 16:1-4, where Paul provides directions for collecting money. Then in 2 Corinthians 8-9 (esp. 8:6, 10; 9:1) Paul exhorts the Corinthians to complete what they have begun. When Paul writes Romans, he is ready to travel to Jerusalem with what has been collected among the gentile believers in Macadonia and Achaia (Rom 15:25-26). Prior to the time of writing Romans, therefore, Paul had already written Galatians, and 1 and 2 Corinthians, in addition to 1 Thessalonians (believed to be Paul’s earliest extant epistle), and perhaps Philippians as well.
Myers writes on the relationship between the ideas in Romans and in his earlier epistles (op. cit., v. 5, p. 817):
Moreover, Romans is heavily indebted to those epistles that have gone before. As G. Bornkamm (1963: 2-14) has rightly pointed out, a number of topics that are present in Paul’s earlier epistles surface in Paul’s Epistle to the Romans. Among those topics are justification by faith and not by the works of the law (Galatians 3-5; Philippians 3; Romans 1-4); the fatherhood of Abraham (Galatians 3; Romans 4); Adam as the head of the old order of humanity and Christ the head of a new order (1 Cor 15:21-22, 45-49; Rom 5:12-19); the church as Christ’s body composed of diverse elements (1 Corinthians 12; Rom 12:4-8); the need to exercise personal freedoms with consideration for the consciences of others (1 Corinthians 8-10; Romans 14-15) – to name only a few. But in Romans, Paul does not merely reiterate these ideas; rather he reformulates and refines them. Romans, therefore, evidences a greater theological maturity than the other Pauline epistles.
Myers comments on the importance of Romans (op. cit., v. 5, p. 817):
The Epistles to the Romans has also contributed significantly to the history of Christian doctrine. Almost every influential Christian thinker has dealt with Romans. Origen, Thomas Aquinas, and Philip Melanchthon, to mention only a few, wrote noteworthy commentaries on Romans. And numerous theological notions have been derived solely or in part from Romans. Augustine acquired his idea of original sin from Romans 5, Luther gained his understanding of justification by faith alone from Romans 3-4, John Calvin obtained his doctrine of double predestination from Romans 9-11, John Wesley got his distinctive teaching on sanctification from Romans 6 and 8, and Karl Barth learned of the importance of the righteousness of God from Romans 1 and 2. In short, this epistle has exerted a powerful influence on all branches of the Christian Church, and its impact on the lives and thought of prominent Christian thinkers through the years has been second, perhaps, only to the canonical gospels.
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Do Romans 7.7 and Romans 2.14 contradict?
As Stanley Stowers (Rereading of Romans) among others have argued, in Rom 2:14’s ὅταν γὰρ ἔθνη τὰ μὴ νόμον ἔχοντα φύσει τὰ τοῦ νόμου ποιῶσιν, the dative φύσει goes with τὰ μὴ νόμον ἔχοντα (i.e., ‘not having the law’), not with the τὰ τοῦ νόμου ποιῶσιν that follows as many translations traditionally render it. Thus the point is that gentiles do not by-nature have the law (i.e., this is just the flip side of what Paul writes in Rom 3:3 and 9:4). It’s another way of writing that gentiles do not have the law by descent or ethnicity. Paul can still write of the law as a part of the high God’s ethnic promise-package to Israel while also elsewhere holding that gentiles have some knowledge of and responsibility to the law (e.g., Rom 7:1, 4-6).
Tim Gallant makes the argument that Paul was not speaking about gentiles/people in general, but about Christian Gentiles. They lack the Torah but show themselves to have a different law by following Christ.
I believe that Paul is referring to Christian believers. (This is also a position taken by N. T. Wright in his commentary on Romans, as well as in his article, “The Law in Romans 2,” in Paul and the Mosaic Law, James D. G. Dunn, ed; see esp. pp. 143-148. I will attempt to provide further defense for this position than Wright has argued for.)

The language of “the work of the law written in their hearts” in verse 15 is too reminiscent of the promise of the new covenant in Jeremiah 31:31-34 to be merely coincidental. In the LXX, Jer. 31:33 (actually, 38:33 in the LXX; 31:33 is the place of the passage in Hebrew and English) says, “I will give my laws unto their understanding, and upon their hearts I will write them.” The Hebrew can be rendered, “I will give my law in their midst, and upon their hearts I will write it.” (This raises the difficulty of the usual understanding that Romans 2:14 indicates that the Gentiles in view “by nature do the things in the law”; we will take up this problem below.)
Moreover, this “work of the law written in their hearts” in verse 15 is not stated by Paul to be universal. The clause begins with the indefinite pronoun whoever (Greek: oitines, fromostis). Although this word can function as a simple relative pronoun (who, which), that is not the most common meaning, and certainly not the necessary one. No commentator argues that the “work of the law” here is perhaps non-existent due to the indefinite article, and that is clearly not my point. Rather, I am saying that Paul (1) assumes this work of the law to be a reality; and (2) thinks of it in non-universal terms: only some Gentiles have this work of the law written in their hearts.

Furthermore, the indefiniteness of verse 15 (whoever) matches the indefiniteness of verse 14: “For whenever (Greek `otan) Gentiles who do not have the law…do the things in the law….” Verse 14 must be indefinite, because otherwise we would have to conclude that Gentiles universally “do the things in the law,” at least some of the time.
The parallelism between 1-11 and 12-16 is also echoed in the passages following, in particular 2:25-29, as Wright has so ably shown in his article, “The Law in Romans 2.” This is made most evident in comparing the law-keeping Gentile of verse 14 with verse 27: “And will not the one, by nature uncircumcised, who keeps the law, judge you who through the letter and circumcision transgress the law?”

In conclusion, we may say that Romans 2:12-16 is a passage that we ought to take straightforwardly rather than hypothetically. The doers of the law are those who have found the law’s goal to be Christ Himself, and who thus confess Him as Lord. They are also those who are, in becoming united to Christ, granted His Holy Spirit. They walk by that Spirit, and thus fulfill the true intention of the law (cf. 8:1-14; 13:10; Gal. 5:14-26). The doers of the law will stand uncondemned at the final judgment, because they are in Christ, who has encountered and fulfilled the sentence of judgment when He became their sin offering (8:3-4)
The Jewish Annotated New Testament:
Scholars frequently introduce two distinctions to help make sense of Paul’s comments on the law. The first is one that looms large especially in Paul’s discussion of the law in Romans (2.12–3.31): the contrast between Jews and Gentiles. This particular distinction also operates in later rabbinic law. Building on passages such as Genesis 9.1–17 (and possibly postbiblical traditions such as Jub. 7.20), the rabbis developed a list of seven “Noachide Laws” that constitute the minimal legal obligations imposed on Gentiles. According to one Talmudic listing (b. Sanh. 56a), Gentiles are prohibited from cursing God, idolatry, sexual immorality, bloodshed, robbery, and eating a limb off of a living animal; they are obligated to establish and maintain courts of law. This concept may shed light on Paul’s assertion that some “Gentiles, who do not possess the law, do instinctively what the law requires” (Rom 2.14; cf. 2.21–24). Presumably keeping kosher is not what came naturally to such Gentiles, but avoiding bloodshed, robbery, and perhaps even idolatry could have come naturally to those Paul has in mind.
The JANT note on Romans ch 7:
The language is very difficult to follow: the same terms are used but with different referents and implications along the way, and the prevailing psychological interpretations are themselves suspect. The goal of the argument is evident by the end of it, and in keeping with that which has been argued in the previous chs: it is that these members from the other nations who have turned to God in Christ are not bound to live according to the limitations of their previous identity in Adam, in sin leading to death, but in righteousness, because they now live in Christ. They are not circumcised and so not under Torah, because they are not Israelites, but they are nevertheless now free from the law of sin to live a life such as Torah describes, a life lived according to God’s standards, and not those of sin and death.