Philosophy and Proofs
Atheism includes any philosophy which claims that no God or gods exist, including any rational or reasoning creator of the universe.
Christianity is the philosophy that claims that Jesus of Nazareth is the Son of God and Jewish Messiah (or Christ); that he was crucified, died and was buried, and rose again three days later; that his death was an atoning sacrifice for the sins of his followers; and that placing one's trust in Jesus is how any sinful person can be forgiven and made righteous before their creator.
Deism refers to any philosophy which claims that there is a supreme creator of the universe who has no ongoing involvement with what is created apart from the initial act of creation itself.
Empiricism describes any philosophy which claims that all knowledge originates in experience, denying the validity of both deductive reasoning and divine revelation.
Islam refers to the specific philosophy of the Muslims, a monotheistic and unitarian belief system declared by Muhammad in 610 AD and described in the book known as the Qur'an.
Monotheism refers to any philosophy which claims that there is only one supreme creator of the universe.
Open theism refers to any philosophy which claims that there is a supreme creator of the universe who does not foreknow the outcome of human choices.
Polytheism refers to any philosophy which claims that there are multiple supreme creators of the universe.
Rationalism describes any philosophy that claims that beliefs and opinions should always be logical, deductive conclusions rather than being based on experience, observations, religious teachings, or divine revelation.
Theism includes any philosophy which claims that some kind of God or gods exist.
Trinitarianism is the philosophy that there is only one God in terms of essence or being; and that the one God is revealed through three eternally distinct persons, specifically, the Father, the Son (Jesus of Nazareth), and the Holy Spirit. Trinitarianism is unique to Christianity.
Unitarianism refers to any philosophy which claims that divine sovereignty is not shared in any way.
In Printed Form
Along with numerous other authors including Don Landis, Bodie Hodge and Roger Patterson, Timothy McCabe contributes analyses of various world religions and cults in this volume from Master Books.
"How does your belief system, and the authorities upon which it is based, guide your behavior?"
The Bible teaches in Matthew 22:36-40 that all of God's laws for humanity depend upon obedience to the following two commands: 1. Love God. ("Love the Lord your God with all your heart and with all your soul and with all your mind.") 2. Love your neighbor. ("Love your neighbor as yourself.") The most important thing to note here is that love for God must always come before and have total priority over love for other people -- otherwise we fall into idolatry.
"Why does God allow charlatans to use His name to extract money, sex, attention and even their very lives from devout believers, who truly, honestly believe that they are listening to the word of God?"
There are several assumptions made in this question. The first assumption made, is that God actually does this. I'm not convinced that God does do this, because I'm not convinced that these things happen as described. I haven't seen any evidence for it. Granted, this website does not allow for very lengthy questions that could include evidence, but regardless, my point is that I see absolutely no reason to accept the question as asked.
"Is Buddhism compatible with Christianity?"
Buddhism is incompatible with Christianity. Buddhism rejects the concept of a permanent self, or an immortal soul. In Christianity, the concept of "self" and the immortal soul are pervasively important. In Christianity, it is "self" that sins (Ezekiel 18:4), is resurrected (John 5:29, Romans 8:11), and is eternally judged (Matthew 7:23, Revelation 14:11). It is "self" that is offered eternal forgiveness through Jesus Christ (John 3:16).