UPDATE:
If you believe the Bible, then:
1) True.
2) I personally have never seen any issue arise which could not be addressed by something in the Bible. That is my personal experience, however, and may not hold true for everyone.
3) See 2.
If you don't believe the Bible, then the question is moot. If you do not believe that the Bible is true, then you lack the primary foundation upon which to build Christianity, and thus cannot claim to be a Christian.
Old Answer:
While many would argue blindly that it is, especially using Revelations 22:19, which says, "And if anyone takes words away from this book of prophecy, God will take away from him his share in the tree of life and in the holy city, which are described in this book." (NIV), no book in the Bible claims the sole authority of God. At the time the Book of Revelations was written, there was no "Bible", but rather Revelations was sent out as a letter to the churches along a mail route.
Galatians 1:8-9 repeatedly asserts that if anyone teaches anything other than the message that Paul had preached, they should be eternally condemned. This does not claim the sole authority of God, but rather gives us a standard by which to measure anything else: "Does this teaching contradict the teachings of Paul and/or the words of Christ?"
For this reason, Christians should study the Bible in order to know for a surety if something does or does not contradict its teachings, but the Bible as we know it was not compiled until many years after the individual books were written. Prior to that time, it was simply a collection of letters along with the "Law and the Prophets" which we know as the "Old Testament".
If you cannot believe in the Bible, then you have no basis upon which to rest your faith. When I say "study" the Bible, I don't just mean what the current English translation says, I mean for a person to dig into the history, the culture, and the original languages of the Bible as well.