You have to understand that at the time, the church in Rome was wrought with arguments between Jewish believers and Roman (gentile) believers. Each side was accusing the other side of being unrighteous and Paul wrote this letter to address some of the concerns. The verse you quoted is in a section where Paul is instructing the Christians to remember that God judges all - no one is righteous.
Look at it this way: the things people do are a mirror to ourselves. So when you do pass judgment on another, remember Psalm 139:23-24, "Search me, O God, and know my heart; test me and know my anxious thoughts. See if there is any offensive way in me, and lead me in the way everlasting."
Pass judgment but then repent for your own sin and use it as a lesson for yourself as much as for the other person.
I confess, I did not really go into reading the verse when you first presented it. You can cross off #2 as well and I just answered #1 in a roundabout way. He was talking to both the Jews and the Romans but the Bible is timeless - it is a lesson for ourselves as well.
I also feel that you can cross of #3 as well (however, keep in mind that #3 is really a summary of the passage as a whole and in fact, the entire Book of Romans). The verse you quoted seems to read more about the "law" (the law as Jesus). So one who hears the "law" and then believes the "law" (that is, Jesus) is given a reward of eternal life. Those who hear the "law" but do not write the "law" upon their hearts, is therefore their own law. If they are their own law, then they are unrighteous in God's eyes. This is the passage people quote (or rather, verse 14) to explain lawlessness and unrighteousness for unbelievers. Believers hold to a higher law but non-believers make up their own laws as they go along. When you think about it, it's actually true. As believers, our conviction comes from God but for non-believers, the only law they follow is the law of the land. Even so, if they disagree with the law of the land, they will do their own thing. Look at something as simple and innocent as pirated music downloads. Non-believers can make the claim that they are taking from the rich or that they are helping the poor artists with free marketing or even find equivalent loopholes with other media (such as photocopying of textbooks, fair-use, etc.). But for Christians, we hold to a higher law. The Holy Spirit convicts us - no matter how one looks at it, even if a believer disagrees with the MPAA's practice of robbing artists of their hard-earned money, the Holy Spirit convicts. Stealing is stealing. I have yet to see a Christian not squirm in their seat when told this straight up. Even Christian teens feel convicted; they may ignore the conviction but they know deep down that they've just been convicted.
Ok, I guess I went overboard... I summarized the entire passage instead LOL
Just take this rule of thumb: God uses the humble to do His work. The humbler you are, the better. Look at Moses - God loved Moses because Moses was very humble. That doesn't mean you can't correct other Christians but when you do, remember that you may have done the same thing you are correcting in another. After you remember, correct yourself as well.
