"If that is what you mean by "Faith," then yes, it's by Faith. And all of these elements comprise this Faith in its fullest definition."
All these points comprise being "incorporated into Christ." If that's what you mean by Faith, then we're on the same page. Yay! Handshakes all around.
But a great many people, when they say "faith," actually just mean "intellectual assent," so we have to remember that James (who has the same authority in the Holy Spirit as Paul) says, "Faith without works is dead."
And we have to remember that Paul agrees with James; for Paul himself said, "if I have all faith, so as to remove mountains, but have not love, I am nothing." But I'm truly glad we're in agreement on that.
Of course there are going to be those but we need to understand that it is God who calls and works within those who "intellectually assent". There are those also who work the works with no faith. I could give you the example of Mother Theresa because she claimed it didn't matter what religion you were. She claimed you could be a better Buddhist, or Hindu, or whatever.
Salvation is through faith in Christ shed blood alone. If that faith is genuine it is the Holy Spirit working through that person that will produce the change and the "works" will be exhibited.