Comment: answers. & You're welcome

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answers. & You're welcome

Regarding: "What does he mean by righteous? Does he mean following the 10 Commandments?"

God is holy, and holiness is pure, it is to be apart from everything that is unholy. In the gospel of Matthew 5:48, Jesus said: "You therefore must be perfect, as your heavenly Father is perfect."
Matthew 19:16-22 describes someone asking Jesus what they need to do to have eternal life, and Jesus does point the man to the 10 commandments, but to make the point that he hasn't kept them even though he thought he did. Paul explains more about the purpose of the Law in "Galatians". I would recommend reading the entire book of Galatians, as it is only a few chapters. Here are a few quotes from it:
Galatians 3:10-11 "For all who rely on works of the law are under a curse; for it is written, "Cursed be everyone who does not abide by all things written in the Book of the Law, and do them." Now it is evident that no one is justified before God by the law, for "The righteous shall live by faith."
Galatians 3:24-28 "So then, the law was our guardian until Christ came, in order that we might be justified by faith. But now that faith has come, we are no longer under a guardian, for in Christ Jesus you are all sons of God, through faith. For as many of you as were baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus."

Basically, the Law is like a mirror which shows us that we are sinful, but looking at a mirror all day will not make you clean when you are dirty. It will only testify whether or not something is clean. Likewise, Paul argues that the death of Jesus on the cross pays the debt for our sin and makes us righteous in God's sight when we place our trust in Jesus as the sole means of our salvation. Romans 3 is reiterating that everyone is in need of Jesus to make them perfect in God's sight, by pointing out that nobody has kept the law perfectly. Jesus was sinless and lived the perfect life of love. By our trusting in his payment for our sins, his perfect righteousness is "imputed" to us, as if it was credited to our account(Romans chapter 4 discusses this). Then we can be perfect in God's sight because of the perfect righteousness imputed to us through the cross, even though we personally might fall into sin on occasion. Those who trust in Jesus are promised the holy spirit, and will be progressively sanctified and will turn from sin more and more as they grow in the knowledge and grace of Jesus.

Regarding: "The part I really don't understand is "they are together become unprofitable" what does that mean, it seems like an odd choice of words?"

Ideally, whenever someone gives a scripture reference, if you are interested enough to consider it, you should really go back to the source of the quote and read the entire chapter (or previous and following chapters as well, and preferably the entire book) in order to get the context. I was quoting the King James Version, but a more modern translation(NASB, ESV, NKJV, etc.) might be easier to understand. If reading the context and checking other translations isn't helping, commentaries are a great way to gain insight. I've included a number of excerpts from commentaries on the part you found most difficult, But I would recommend reading Matthew Henry's commentary on the entire chapter if you want to get a fuller sense of what is being communicated, as Paul's letter to the Romans is drawing upon Old testament passages to make some points about Christian theology. Here are the quotes about your question:

Barnes:
"They are together - They have at the same time; or they have equally become unprofitable. They are as one; they are joined, or united in this declension. The expression denotes union, or similarity.
Become unprofitable - This word in Hebrew means to become “putrid” and “offensive,” like fruit that is spoiled. In Arabic, it is applied to “milk” that becomes sour. Applied to moral subjects, it means to become corrupt and useless. They are of no value in regard to works of righteousness.
"

Gill:
"they are together become unprofitable; the word נאלחו, in Psa_14:3 and Psa_53:3; is translated, "they are become filthy"; which R. Aben Ezra interprets by נשחתו, "they are corrupt"; and R. Solomon Jarchi by נהפכו לקלקול, "they are turned to corruption"; the metaphor is taken from stinking flesh, which is tainted and corrupted, and so good for nothing, hence here rendered "unprofitable"; for so men being corrupted by sin, are of no use, service, and advantage to God, to men, or to themselves; but, on the contrary, nauseous to God, and to all that are good, and hurtful to themselves and others: for ..."

Henry:
"They are together become unprofitable, Rom_3:12. Those that have forsaken God soon grow good for nothing, useless burdens of the earth. Those that are in a state of sin are the most unprofitable creatures under the sun; for it follows, "

Clarke:
"They are together become unprofitable - ηχρειωθησαν. They are useless, good for nothing; or, as the Hebrew has it, נאלחו neelachu, they are putrid: he views the whole mass of mankind as slain and thrown together, to putrefy in heaps. This is what is termed the corruption of human nature; they are infected and infectious. What need of the mercy of God to save from such a state of degeneracy!"

Wesley:
"They are become unprofitable - Helpless impotent, unable to profit either themselves or others."

Vincent's word studies:
"They are together become unprofitable (ἅμα ἠχρειώθησαν)
Only here in the New Testament: Together carries forward the all. The Hebrew of the Psalm means have become corrupt. The Greek word is to become useless. Compare Joh_15:6."

Robertson's Word pictures:
"They are together become unprofitable (hama ēchreōthēsan). First aorist passive indicative of achreoō. Late word in Polybius and Cilician inscription of first century a.d. Some MSS. read ēchreiōthēsan from achreios, useless (a privative and chreios, useful) as in Luk_17:10; Mat_25:30, but Westcott and Hort print as above from the rarer spelling achreos. Only here in N.T. The Hebrew word means to go bad, become sour like milk (Lightfoot)."

Also, if you want to study on your own, you can get free bible software with all sorts of commentaries, translations, language resources, lexicons, etc. http://www.e-sword.net/ is a nice one for the PC.

Regarding: "Something else that bothers me is the word God spells dog backwards, that doesn't seem very nice name for our Creator, that word just doesn't seem right."

"God" is just an English word. In German it would be "Gott". The German word for dog is "Hund". In German "ttog" doesn't mean anything. God is a generic term like "man", not a name.