How would you in your opinion define "once saved, always saved"?
Once a child is adopted it is always a child of that individual. Even if it brings shame or condemnation to the family, it is still their child. The father will chastise that child. Life may even be hard for that child due to the father's admonishment, and disapproval of the child's actions, but it is still his child.
Is it true or is it false doctrine?
I believe it to be true.
Would "wilful sinning" have any connection to this said doctrine"?
All sin is willful. There is no accidental sin. Sin is rebellion. Don't give yourself that 'out'. When you sin, you do so on purpose. You know what you're about to do. You know it is wrong, and you do it anyways knowing it is wrong. We push away God, justify it and make all manner of excuses to allow ourselves to sin. We expend serious effort to engage in theses acts. Create motives, lies for cover, and even stories to clear our tracks. If you ever sit down and think about how much effort goes into sinning, it is a real ordeal to undertake. We even lie to our friends and loved ones, because we do not want them to find out what we have done. We have shame, and embarrassment for our sin, and yet chose to do it again.
Temptation is a crutch we blame, and a scapegoat we slay for our own actions. It is written there hath no temptation taken you but such as is common to man, but God is faithful; who will not suffer you to be tempted above that ye are able, but will with the temptation also make a way to escape; that ye may be able to bear it.
Don't cop out. Take God's escape.
How also about works or obedience?
This speaks to honoring God. Pleasing him, and making him proud of you.
Babies need diapers, teens rebel, and new adults on their own have no idea what is laid before them. All of them lack the knowledge, the wisdom, and the understanding that comes with maturity. A father no longer has to chastise a person that is no longer their child. That being said there's no use for scripture that tells us to not despise god's chastisement if we are no longer his child after sinning.
Even in James where we are told to continue in the perfect law of liberty. And to be a doer not a hearer only. We first must hear. We first need the understanding of what it is we have learned, and then in maturity, with the wisdom of God we can live pleasingly to God. Honoring him with our lives and actions. This doesn't happen over night any more than a newborn becomes a grown man in a day.
As new babes, We need protection from our own ignorance. We do not know it is bad to put a fork in a electric outlet. We do not know these brightly colored pieces of candy Mommy uses to wash clothes are deadly poison. We will put em right in our mouth. As a child we learn our families rules, and ideals. We are taught that the world is not always safe, fair, and can be cruel. We learn friendship, compassion, and love. We begin the understanding we need for adulthood. As teens, well forget it... we already know everything. Our bodies don't fit our minds. We do not understand our own emotions or insecurities, but our parents definitely have no clue. As young adults we are finally free. Were on our own for the first time and find new independence brings new responsibilities along with it. We quickly understand why our father did what he did and along with that comes respect, or we rebel. Go our own way....
Now mind you, it is impossible to please God without faith and works. However before coming to Christ you have done neither. No matter how good you were before coming to christ you cannot please God without first having faith in his son. So, even as we find it in scripture, God loved us before we loved him.
What roles if any would that doctrine play in how we will end up in eternity?
Only one thing at all means anything at all to me. I confess Jesus Christ. I confess that Jesus is the word of God come in the flesh that dwelt amongst men. Jesus is my salvation. I can neither save, nor condem one individual; including my own self. Only Jesus can. That being said, my understanding of Jesus is not as important as Jesus's revelations of himself. That comes with maturity, and effort.