Were the people, whom Jesus healed while walking the earth, spiritually dead?
Well, the Bible doesn't tell us about all of them. We do know the ones who He affirmed as having faith in Him/His ability to heal, were already regenerate i.e. the woman with the issue of blood, the Centurion's servant, the paralytic in Matthew 9:2.
You aren't trying to bait me are you?
(I do apologize, the wording does sound like baiting. That was not my intention.)
Where does the Scripture affirm they were regenerate? The Matthew 9:2 verse you use shows the man's sins are forgiven, but it doesn't say anything about regeneration...
There appears to be four key elements to salvation;
1. Justification - the forgiveness of sins
2. Regeneration - made into a new creation
3. Sanctification - made into the image of Christ
4. Glorification - our lowly bodies made like Christ's glorious body
Matthew 9:2 only says that the man's sins were forgiven, to say that he was regenerated, (my opinion), is reading too much into the Scripture. As for the other individuals you referred to, Jesus only affirms they have faith, to say faith eqauls regeneration is reading into the text, not pulling from it. Unless you can show me otherwise...
Faith means: Hebrews 11:1
"Now faith is being sure of what we hope for, being convinced of what we do not see."
Faith is hope that what we read in Scripture, will come to pass. God tells us that when we come to Him in faith, He will save us.
This is fascinating to study
"For by grace you are saved through faith, and this is not from yourselves, it is the gift of God; it is not from works, so that no one can boast."
Calvanist seem to use the above Scripture to say that faith is given to us by God, it is not a choice for us to believe. But I'm not sure I see what they see. When the passage says, "and this is not from yourselves...," it isn't refering to faith, but to, "For by grace you are saved..."
Just as Jesus healed those individuals, God saves us. Jesus is the one that healed them, and there was no way they could heal themselves. In His grace, He chose to heal them, and to do it through their faith.
"But when Jesus turned and saw her he said, 'Have courage, daughter! Your faith has made you well.' And the woman was healed from that hour."
In the same way, there is no possible way for us to save ourselves. It is a free gift from God who chooses to give it to all who come by faith.