In particular, is it sin when someone:
?
What is the relationship between sinful behavior and sin?
Nowhere in the Bible is something sinful not sinful because of how someone feels. There may be things that are not innately sinful, that may be sinful in certain situations (Ecclesiastes 3).
In your questions, specifically when someone:
does something sinful, but he is not aware of the sinfulness
For if we sin deliberately after receiving the knowledge of the truth, there no longer remains a sacrifice of sins, but a fearful prospect of judgment, and a fury of fire which will consume the adversaries. A man who has violated the law of Moses dies without mercy at the testimony of two or three witnesses. How much worse punishment do you think will be deserved by the man who has spurned the Son of God, and profaned the blood of the covenant by which he was sanctified, and outraged the Spirit of grace? For we know him who has said, 'Vengeance is mine, I will repay,' And again, 'The Lord will judge his people.' It is a fearful thing to fall into the hands of the living God. (Hebrews 10:26-31)
Note the verse that says "there no longer remains a sacrifice of sins". This verse points out that those who sin when they know they are sinning, will receive a "fearful prospect of judgement". This implies that sinning when you are not aware of your sin carries a lesser penalty (although still, all sins are enough to send a man to hell). See this article.
does something sinful, someone told him it is sinful, but he still doesn't feel it as sin
You seem to be presenting two different possibilities here:
He does something sinful, but he doesn't feel it is sin - If he is doing "something sinful", that is, something specifically called out in Scripture as sin, it doesn't matter how he feels on the issue. Indeed, the rejection of that action being sin is another sin, a rebellion against God.
He does something that someone else has told him is sinful, but he doesn't feel it is sin - "Be a Berean" and search the Bible for backing to that action being sin. If none exists, or can be reasonably inferred, and you are not convicted that that action is sin, they you're probably fine. If there is backing in Scripture, then this falls back under (1) and is of itself sin.
does something not sinful, but he feels it as sin
Therefore to him that knoweth to do good, and doeth it not, to him it is sin. (James 4:17)
But whoever has doubts is condemned if he eats, because the eating is not from faith. For whatever does not proceed from faith is sin. (Romans 14:23)
See this article, but it seems to be yes. If you truly believe something is sin, even if it is not specifically presented as such in Scripture, and you sot what you believe is wrong, then you are sinning.
Overall, the relationship between sinful behavior and sin is this: sin is the doing of anything that God prohibits, the failing to do something he commands, or the disobeying of your own convictions about sin, while sinful behavior is the engaging of the act of sin, but may be the engaging in an act that is not inherently sinful, but is for that particular situation.
