Where is my way out

I've been thinking a lot about faith lately.

I've been doing bible study every Friday for about 8 months. And somehow I feel it comes to a stage to ask myself, Am I a Christian? The more I wanna talk about it, the less I could say. Pieces of thoughts just come and go in my mind, but I can't find an outlet or some way to sort them out.

It is common to consider someone a Christian if he could answer all yes to the following questions:
Do you believe Jesus Christ is the Son of God?
Do you believe that you are a sinner?
Do you believe he had to die for your sins?
Do you believe he resurrected after 3 days?
Maybe there are more questions or questions in different angles. These are what I've heard most frequently.

I think again and again about these questions. But I don't know how to answer. Truely that they are just simple yes and no questions, but when it comes to 'believe', it's hard to tell. I could say I know the answers have been written in Bible, and I am willing to believe Jesus died for us by his holy will. But did he HAVE to die for my sins? I feel blank. I don't know how to connect myself, or my sins, to his death. And I don't know how the reason he laid down his life for us
is gonna affect my life now.