When someone tells you what you think...it wastes too much time trying to correct the wrong impression instead of getting on with the topic at hand. I wasn't insulted.
Yes, God's grace is open for all to take advantage of or deny.
We cannot add to God's grace in any way...God is full of grace - one cannot be more full than full.
The following verses about God's mercy (which is a part of His grace) tells that all are welcomed:
Isaiah 30:18
18So the LORD must wait for you to come to him
so he can show you his love and compassion.
For the LORD is a faithful God.
Blessed are those who wait for his help.
The above shows that God is waiting for us to go to HIM...again, we are able to seek God.
And then He will have love and compassion for us.
Psalm 86:15
15But you, O Lord,
are a God of compassion and mercy,
slow to get angry
and filled with unfailing love and faithfulness.
Matthew 5:4
“Blessed are the merciful, for they shall receive mercy.
so many more...
Our faith is not something we produce. Faith is already available to us as a gift from God.
The difference between the reformed and the rest of Christianity is that they believe faith is given to a select few,
whereas God's faith is available to all.
I've said before that Ephesians 2:8 is understood to mean that all mentioned are gifts: Grace, Faith, and Salvation
As to the living...it is the Holy Spirit that lives in us.
Everyone believes this...I won't even post anything since the alternative you state (we live in HIM) is not believed by anyone.
As to cooperation:
Yes. Our WALK with God is a cooperation between what we do in our lives and what God would have us to do.
I said OUR WALK with God. Please don't reply that I'm saving myself.
What could be debated is whether or not we have anything to do with our actual justification/salvation.
I'd have to say that, yes, we also cooperate in our salvation in the sense that God must make the offer of salvation,
and man must reply with a yes or a no.
Revelation 22:17
17The Spirit and the bride say, “Come.” Let anyone who hears this say, “Come.” Let anyone who is thirsty come. Let anyone who desires drink freely from the water of life.
We're invited by God in some way or other - each in a different manner.
So God's grace calls to our heart, as God calls to everyone, and we must reply.
Matthew 23:37 Jesus said
37“O Jerusalem, Jerusalem, the city that kills the prophets and stones God’s messengers! How often I have wanted to gather your children together as a hen protects her chicks beneath her wings, but you wouldn’t let me. 38And now, look, your house is abandoned and desolate.
Jerusalem wouldn't LET Jesus protect her.
So now her house is desolate.
Not because Jesus caused it, but because Jerusalem would not have faith in Jesus.
So there definitely is a calling and a reply.