Although scripture clearly teaches that obtaining salvation is not on the basis of works (Romans 4:2-6; 11:6; Ephesians 2:8,9; Galatians 2:16; Philippians 3:9; Titus 3:5; 2 Timothy 1:9 etc..) God's judgment is on the basis of man's deeds whether good or bad. (John 5:28-29; Romans 2:5-11; 1 Corinthians 3:8; 2 Corinthians 5:10 etc..). In Romans 2:5-11, Paul describes the deeds of two distinct groups: the redeemed/everyone who does good and the unredeemed/everyone who does evil.
We reap what we sow, yet salvation is a gift received by grace through faith and not by works. (Ephesians 2:8,9) In Romans 4:4-6, we read - Now to him who works, the wages are not counted as grace but as debt. But to him who does not work but believes on Him who justifies the ungodly, his faith is accounted for righteousness, just as David also describes the blessedness of the man to whom God imputes righteousness apart from works. Those who teach salvation by works typically confuse 'descriptive' passages of scripture with 'prescriptive' passages of scripture. The natural man cannot understand. (1 Corinthians 2:14)
In regard to "doers of the law" in Romans 2, context is important. Paul was talking to the Jews (Romans 2:17-24) about their judging of the Gentiles and then points them to their own law (standard of judgment) and hypocrisy and tells them that the doers of the law will be justified before God (v. 13). That leaves them out, along with everyone else. (Romans 3:22-28; Galatians 2:16; Philippians 3:9) The standard they wanted to measure up to was the law. Paul was telling them that the doers of the law will be justified. So, obey the law, obey all of it, but if you don’t obey all of it, you failed! He tells them that the Gentiles who didn't have the law according to the knowledge of the Jews were instinctively doing the things of the law (verse 14) and will be judged accordingly. How much more so the Jews?
Paul was showing the self-righteous Jews who judged the Gentiles that they were not able to measure up to the perfect standard of the law. They were hypocrites. This is why Paul tells us in the very next chapter in Romans 3:28 that we are justified by faith apart from the works of the law. *No one was able to perfectly obey the law (except for Jesus Christ). If you fail even once (stumble in one point), then you become guilty of all. James 2:10, "For whoever keeps the whole law and yet stumbles in one point, he has become guilty of all."
Galatians 3:10, For as many as are of the works of the law are under a curse; for it is written, "Cursed is everyone who does not abide by all things written in the book of the law, to perform them." The Jews can be justified before God by keeping the Law, but he or she has to be 100% perfect. A person can’t fail even once--ever. But all have failed (Ecclesiastes 7:20; Romans 3:23; 6:23; 1 John 1:8-10), that is why man is justified before God by faith and not by the works of the law. (Romans 3:22-28, Galatians 2:16; Philippians 3:9 etc..)
That is speculative at best. The present tense of the word "justified" implies that these Galatians were contemplating justification by the law. They were getting side tracked by legalistic teachers. "You who are trying to be justified by the law have fallen away from grace," but had they fully come to that place yet? Galatians 3:3 reads: Are you so foolish? Having begun in the Spirit, are you now being made perfect by the flesh? The middle voice implies "making yourselves perfect" by means of self effort. The present tense indicates that the action is in progress and that there is still time to correct the error.
If these Galatians lost their salvation and it was a done deal, then why didn't Paul simply say you "lost your salvation" and I'm done with you? Instead, in verse 10, he said - I have confidence in you, in the Lord, that you will have no other mind; but he who troubles you shall bear his judgment, whoever he is. Why would Paul have confidence in these Galatians if they lost their salvation and it's all over for them? In verse 12, Paul uses hyperbole, As for those agitators, I wish they would go the whole way and emasculate themselves!
2 Timothy 2:19 - the solid foundation of God stands, having this seal: “The Lord knows those who are His,” and, “Let everyone who names the name of Christ depart from iniquity.” Those who believe the gospel are sealed in Him with the Holy Spirit of promise, who is the guarantee of our inheritance until the redemption of the purchased possession, to the praise of His glory. (Ephesians 1:13-14) Movable foundations are based on the wrong foundation. Namely, works righteousness instead of Christ.
In regard to 2 Corinthians 13:5, for those who demanded proof that Christ was speaking through Paul, he turned their challenge around and asked them to test themselves to see whether they are in the faith. Paul trusts that they will discover that we have not failed the test. Sadly though, there are genuine Christians and there are "nominal" Christians. There are genuine believers and there are make believers mixed together throughout various churches and on various Christian forum sites.