The short answer is ‘Yes’ to the question whether all a Christian needs is to have faith to be saved but I would like to clarify what faith actually is. Faith has become a particularly religious word that has lots of different meanings. People have a tendency to talk about faith in and of itself - “Do you have faith?” - and this hides its real meaning.
In the bible the term faith is simply used to mean trust, rely or depend. You can use all these words interchangably. So to have faith in something is to depend upon it, to trust in it or rely on it. For example, you display faith when you sit in a chair. When you sit, you place your trust in it and depend upon it to hold you. It is not your faith that holds you up it is the chair. And here is the most impotant thing about faith - it is not that you have faith, it is what you put your faith in that counts.
When Christian faith is understood in these terms then we see that it not so much our faith that is important but what we place our faith in. Christianity is all about placing faith or trust is Jesus Christ and his death for our salvation. To trust in anything other than Jesus will mean that our faith is wrongly placed and we will not be saved. As Jesus said - “I am the way, the truth and the life, no one shall come to the father but through me” (John 14:6). That is hard for people to hear, but it is the truth.
But it is not just faith though, it is faith in action. Real Christian faith is seen in the way in which we live. If I said I had faith that a chair would hold me but were not prepared to sit in it, what does that say about how real my faith is? It is easy to say I have faith, but the quality of that faith will be seen in the way I live, the way in which I follow Jesus and seek to obey him. It is that sort of faith that saves and is the only “requirement” to claim that you are Christian.
On this basis, then, you can talk about right religion and wrong religions; not in terms of being catholic, jewish or muslim but in terms of whether the religion has faith in Jesus alone at its centre.
People are saved when they place their trust/faith in Jesus. Can a Jew and Catholic be saved, yes if they place their faith in Jesus’ death. If they were to place their faith simply in being a Jew or Catholic then they have placed their faith in the wrong place and have ignored God. Anyone who places their trust/faith in someone rather than Jesus cannot be saved! (acts 4:12)