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.
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.
Pantheism denotes any philosophy which claims that god and the universe are identical.
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.
"Can god make a rock so big he can't lift it?"
No. The God of the Bible is incapable of numerous things. Essentially, all of these things are summed up in 2 Timothy 2:13 which states that God "cannot deny Himself". The God of scripture is a logical God, which is the only reason why the laws of logic, such as the law of non-contradiction, can be trusted to be universal and invariant.
"How is God any different than Santa Claus?"
This is sort of an odd question as there are so many very obvious differences. For example, Santa wears a red hat, whereas God doesn't have a physical head to put a hat onto. I don't know of any religion or worldview that claims that God climbs in and out of chimneys, either. There is, in this question, an implicit attack on theism. However, it is quite possibly one of the silliest attacks on theism I have ever encountered, and I encounter it rather frequently.
"Should modern mainstream religions be considered cults?"
Modern mainstream religions could be considered "cults", and every form of Atheism could as well. But why should it matter if that particular term can be applied? Why would we want to call every modern mainstream religion a "cult" apart from a desire to provoke some type of defensive emotional reaction from religious persons? And why would anyone be interested in manipulating such a reaction?