Very good questions!
Let me give quick answers, then dive in deeper. Please ask further if you require further clarification.
By believing in God. (John 3:16, and many places).
Old Testament people had to look forward to a day for God's salvation.
People in Jesus' time could look to Him to believe. (John 6:29, and other places)
Today, we are given the Holy Spirit who reminds us of what God has done (John 15:26).
But simply, it is to believe that we cannot do it on our own, and are utterly helpless. Then, we would only rely on God, and that leads to repentance and true trust in God. Only when we can completely trust in God, can we say that we are saved.
Yes.
Historically, this is a very debated question. Even today, Calvinists believe in predestination (God chooses us), while Arminians (Methodists, Wesleyans, etc) lean toward free will.
I say neither are useful arguments. Instead, look at it this way: God, who knows all things, knows who will come to believe in Him, and who will not.
Throughout Scriptures, what you see is human nature that says I can do better without God, from Genesis all the way to Revelation. Yet, there are pockets of people who journey out from the majority. Consider Noah building an ark up on the highest mountain while others laughed at him for his "non-sense." Abraham abandoned his riches to go to a place he didn't know. The slaves of Exodus sought out for the promised land. Even then, we see very few pockets of people who come to fully trust in God. Even those who saw miracles, like beating a huge army with few resources or seeing water and food in the desert, majority also did not believe in God. We see even at time of Samuel's leadership, the people turned away from God saying they want to be like other nations and have a king. All throughout history, we see only a pocketful of people truly believing in God. It is much like today, where many church-goers probably do not fully trust in God or have a relationship with Him.
All that to say, there is free will to choose. But our (human) default state is to trust ourselves and turn away from God. Then, it is the question to ask: do you trust in God fully with your entire life? If so, you are chosen by God. But if you, when you hit your riches, and have other ways of solving life's problem, and you are ok living without God at times, then you know it is your free will that turns you apart from God. God would know our end.
Salvation is not earned. It is a gift of God. So, the faith (trust) in God I spoke about above is not something that we can have on our own. We can try to will our trust in God, but we will likely turn to our own ways by our default mindset. And so, God needs to gift us the ability to believe (Mark 9:24, Ephesians 2:1-10, and many other places show we need help to trust in God).
So, can you lose this gift? A person who has come to faith in God will always be brought back. The Holy Spirit will remind the person about the judgment of sin and they will turn back to God (John 16:8). If the person doesn't mind sin in their lives and holiness is not a major concern to them, they probably never had faith in God in the first place.
This might be very hard to understand if you have been churched for much of your life, and that's why Jesus goes through this dialogue over and over with the pharisees and other religious leaders (Read the book of John). There are many church attendees today, especially those who have attended for a long time who believe they are Christians today. In fact, I think 80% of the US population believes they are Christians.
One key factor to know one is saved is they love God and others. This is shown in their lives because they prioritize spending time with one another, especially other believers, above work and accomplishments.
I don't know where you are geographically, but if this bothers you, I'd love to hold Bible studies with you. We have a few going on, and perhaps you can join us. Or feel free to ask further. I'd love to help!
Dublin, OH
