What you said is a contradiction.
You said,
#1. I believe we receive grace according to what type of faith we have. I don’t believe that a “dead and useless or barren” faith is a saving faith. I believe faith that produces works is a saving faith.
#2. Works play no part in our receiving grace otherwise grace is no longer grace.
You said we receive grace according to the type of faith we have. Yet, you say works play no part in our receiving grace. You are contradicting yourself.
Also, when you quote Romans 11:6 that says, "And if by grace, then
is it no more of works: otherwise grace is no more grace.": You have to realize that Paul is talking to Jews in verse 1.
"I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham,
of the tribe of Benjamin. " (Romans 11:6).
According to Jesus, the Pharisees (Jews) ignored the weightier matters of the Law like love, FAITH, justice, and mercy (See Matthew 23:23, and Luke 11:42).
In fact, the Jews were trying to deceive Christians into being circumcised in order to be saved. We see this heresy mentioned in Acts of the Apostles 15:1, Acts of the Apostles 15:5, and Acts of the Apostles 15:24. This heresy was also alluded to in Galatians 2:3, Galatians 2:3, Galatians 5:2, Galatians 5:6, Galatians 6:5, 1 Corinthians 7:18-19, Romans 2:28-29, Romans 3:1, Romans 4:9-12, Acts of the Apostles 21:21. So if someone is trying to say that they FIRST need to be circumcised to be saved, they are making salvation all about works. This would be "Works ALONE Salvationism" under the Old Law (that is the Old Contract) and this would not be the necessity of works (from the commands in the New Covenant) that follow God's grace (with Grace being the entrance and foundation of our faith). So in passages like Romans 11:6, Ephesians 2:8, and Titus 3:5, Paul is talking against Works ALONE Salvation that did not include God's grace as the entrance and as the foundation of our faith. Paul clearly taught the necessity of works as a part of salvation.
Paul says,
"They profess that they know God; but in works they deny
him, being abominable, and disobedient, and unto every good work reprobate" (Titus 1:16).
"For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live" (Romans 8:13).
"If any man teach otherwise, and consent not to wholesome words, even the words of our Lord Jesus Christ, and to the doctrine which is according to godliness; He is proud, knowing nothing, "(1 Timothy 6:3-4)."
James says,
"...God resisteth the proud, but giveth grace unto the humble." (James 4:6).
Paul says,
“...God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth” (2 Thessalonians 2:13).
"If any man love not the Lord Jesus Christ, let him be Anathema [i.e. accursed]..." (1 Corinthians 16:22).
Jesus says,
"If ye love me, keep my commandments." (John 14:15).
“If ye keep my commandments, ye shall abide in my love; even as I have kept my Father's commandments, and abide in his love.” (John 15:10).
Paul says,
“For if God spared not the natural branches, take heed lest he also spare not thee. Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off.” (Romans 11:21-22).