1) Basically.... Salvation means being saved from eternal ****ation. Those who are "saved" will be in heaven one day. If you want to get more complex, christians have all sorts of differences in interpretation about who is or is not "saved," what constitutes salvation, etc. Some believe in a OSAS doctrine-- "once saved always saved." Under that doctrine, once an individual accepts that christ is his savior, then the individual is saved. The majority of Christian denominations do NOT teach OSAS. Some teach that salvation can be lost. Some teach that if an individual continues to live in sin following their decision to follow Christ, then they were never saved to begin with. Etc. Some church have a set of acts that one must follow in order to be considered saved (i.e. baptism). Other say that acceptance of Christ is enough. The list goes on.
If you want to make the anology to Islam, in order to better understand it, "salvation" for christian would be like the moment that a muslim pronounces the shahada. At that moment, just as an individual is counted as a muslim, in christianty the repentance of sins and declaration of faith is the moment of "salvation." Just as in Islam, it is the moment that the slate is washed clean and the individual is a new creation, pure, sins washed away.
After that point is where the beliefs separate. Very few teach that moment alone is salvation, and from then on the individual is saved. The Bible speaks of working out ones salvation with fear and trembling. It also speaks of faith without works is dead. And there are a number of other things. But it does say that the law is not what saves man. It is through faith that man is saved.
2) Every christian believes in it, but that does not mean that every "christian" is "saved." No one is born a Christian. Every individual must reach a point in his or her life where they make a decision to accept Christ as savior and follow him. Even those who were raised in church and believe they were just "always saved" or "always a christian" must still reach that point in life of making a decision.
When I say that not every "christian" is "saved" it goes back to what I was talking about a moment ago. The Bible says that there are those who will cry "Lord. Lord" and he will say "I knew you not." There are those, it says, who will say we have cast out demons in your name and prophesied in your name, and he will say "I never knew you." The Bible is clear that not everyone who claims to believe in Jesus will be saved. I'm sure that everyone who reads my post will be able to readily think of at least one individual who claims to be a Christian, yet produces bad fruit. I use the word "fruit," because the Bible tells us we will know them by their fruits. A good tree does not produce bad fruits and a bad tree does not produce good fruits. We all have sinned and have a sin nature, but someone who has truly made a decision to follow Jesus does not delight in iniquity, nor follow after sin.
3) Eternal death/ hell is the punishment of non-believers, because they have chosen to reject God. It is no different than in Islam when they say that those who reject God will be punished in hell. In Christianity, you will get differences of opinions about death, hell, etc. Some will say that unbelievers go to hell for all eternity. Some point to in Revelation where it speaks of the final judgment where even those in hell will be judged again, and then their fate will be sealed (which implies that one could actually not stay in hell for eternity, and could escape it at that time, or at that time would be case forever into the lake of fire). (Perhaps it is similar to the Jewish concept of a purging by fire for a time, but I won't presume to know exactly what the author was thinking of when he wrote it.) Some Christians believe that some Jews will also be saved, others teach not unless they accept Jesus as savior. Overall, the teachings are varied.
Your question asked why "death" is the eternal punishment, and don't Christians believe in hell. The author of the website probably was using "eternal death" to mean "hell." The Bible uses a variety of terms. Sheol, Abbadon, Gehinnom, bottomless pit, lake of fire, etc.
Many Christians simply believe in a heaven and a hell- and an individual goes to one or the other after death. I think the reason most Christians believe this way is just for simplicity's sake. The whole of it all is much more complex. Some believe in a type of soul sleep (in the "grave") until the judgment. Most believe individual's go directly to one or the other.
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