Please shed light on the things that somehow make me feel uneasy. How should one know that he is already saved? Is it while we are still alive or when the judgement day appears that we can know we are saved? Thank you very much.
I am afraid that this is a bit of a tricky question. The answer may even be a bit confusing for you. I hope not. I believe that, as Christians, in one sense we are already saved, but in another sense, our salvation is still in the future. There are many aspects of being in the Kingdom of God which are "already, but not yet."
For example, we have been raised from the dead already, if we are Christians (Romans 6:2-4). But in another sense, our resurrection still lies in the future (Romans 6:5-7). We have been raised with Christ already, but in another and greater sense we will be raised with Christ in the future. If we are Christians, then we are part of the kingdom of God already, but not yet. There is a sense, at least, in which those who are in the Church are in the kingdom of God, but the Kingdom of God will only be completely fulfilled when Jesus comes back and the new heaven and earth are brought forth (Revelation 21). We will be in the kingdom in a more complete way at that time.
If we are in Christ, then we have received our salvation (1 Peter 1:9), yet we wait for our salvation. (Heb 6;11-12, Hebrews 10:35-36). John said that he wrote 1 John so that we could be confident of our salvation (1 John 5:13), yet he warns against losing our salvation. Paul warns us on Philippians 2:12-13 to work out our salvation with fear and trembling. Ephesians 1:13-14 tells us that those who have the Holy Spirit have a guarantee of salvation, yet Hebrews 10:26-31 is a warning that we could lose the Holy Spirit (and therefore our salvation).
To summariize, I believe that we can be confident that we are saved if we have obeyed the gospel and been faithful. We can rest assured that we are saved. Yet, for those who are saved, if we ignore so great a salvation (to paraphrase the Hebrew writer) we can lose what we alread have. This is the theme of Hebrews 3 and 4. The conclusion of the Hebrew writer is that for those of us who are saved, if we remain faithful until the end, we can be absolutely confident of our salvation. If we take the advice of the Hebrew writer, we will make it. You do not need to live in constant fear of losing your salvation. On Judgment Day, if you have remained faithful to Jesus to the end, you can be extremely confident of your place with God. However, I strongly advise you not to take this salvation for granted.