Salvation is by grace through faith; and that not of ourselves: it is the gift of God: not of works, lest any man should boast (Ephesians 2:8-9).
Works Alone Salvationism. For a man who boasts in his works in being saved is not doing works of faith after being saved by God's grace. Paul mentions the necessity of works of faith in Ephesians 2:10. But he says in Ephesians 2:8-9 in how we are initially and ultimately saved. Paul says in Romans 8:13 that works of faith (not works of the Law) do play a part in our salvation. Paul says in 2 Thessalonians 2:13 that God has chosen us for salvation by two things. Belief of the truth and by the Sanctification of the Spirit. Paul says in Romans 11 that if you continue in his goodness: otherwise you can also be cut off like the Jews.
It is not by works of righteousness which we have done (Titus 3:4-7).
Correct. Again, it is talking about Works Alone Salvationism. We are not saved by Works Alone but we are ultimately saved by God's grace and His giving us a new heart; But if you were to skip back a chapter, it says,
11 "For the grace of God that bringeth salvation hath appeared to all men,
12 Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world; " (Titus 2:11-12).
Titus 1:16 says we can deny God by a lack of works.
So yes. You need works, too.
The righteousness of God is imputed to us apart from works (Romans 4:1-8).
The works of the Law of Moses and not the Laws of Christ.
Romans 3:1 says, "What advantage then hath the Jew? or what profit
is there of circumcision?"
Why else do you think Paul makes his point involving circumcision in Romans 4:9-12? Please read Acts of the Apostles 15:1, Acts of the Apostles 15:5, and Acts of the Apostles 15:24. Paul was fighting against "Circumcision Salvationism."
You said:
Grace and works are mutually exclusive when it comes to salvation (Romans 11:5-6).
Who was Paul talking to in Romans 11?
He was talking to Jews.
This is the context.