If someone doesn't know God, they will not be aware that they have sinned against him and will not have faith in him.
Even if a person does know God, depression gets in the way and may make them feel worthless and unworthy of his love. And it is possible for a Christian to have depression; apart from people I have known, the evangelist, David Watson, suffered quite badly from it.
Not if it is a result of something you can't help and is something that you don't normally do - i.e out of character.
Depression is an illness; no doubt about it. Illness comes from the devil - he is the thief who came to steal and destroy. He wants to destroy our bodies, minds and spirits and relationship with God.
Someone who was healthy in body and mind who thought negative, destructive and hateful thoughts against God and other people, and who dwelt on them, would be sinning. Someone who is depressed - i.e mentally ill - and not able to control their thoughts, think rationally and so on, would not, imo.
You are taking that verse out of context and seem to be applying it equally to non Christians.
Unbelievers also sin whether aware of it or not.
They having no faith is sin, so yes it applies to unbelievers whatever is not from faith is sin.
It is a sin to not believe in Christ, if you desire proof of that read in Acts 17 this.
30 Truly, these times of ignorance God overlooked,
but now commands all men everywhere to repent,31 because He has appointed a day on which He will judge the world in righteousness by the Man whom He has ordained. He has given assurance of this to all by raising Him from the dead.”
Regardless of whether they hear or not the gospel, God commands all persons everywhere to repent and believe in His Son. there is no longer any ignorance to be used as an excuse, no longer will God overlook the times of men's ignorance, all will give account to God and God tells us the entire world sins.
Romans 3
19 Now we know that whatever the law says, it says to those who are under the law, that every mouth may be stopped, a
nd all the world may become guilty before God. 20 Therefore by the deeds of the law no flesh will be justified in His sight, for by the law
is the knowledge of sin.
No more excuses, all the world is guilty of sin, especially regarding those who have no faith, for whatever is not from faith is sin, this applies to all the world of men.