1. Do the gods and goddesses of Wicca actually exist?
Well, the question isn't formed properly, either that or it betrays a misunderstanding of Wiccan Theology.
There is only 1 God and 1 Goddess.
I would argue that they are two distinct persons that share the same nature and manifest different aspects of their Divinity.
So yes, any Wiccan will say that the God and Goddess does exist.
2. If they actually exist, how do you know they exist?
There are many ways to know the divine exists. I hold the view that belief in the Divine is properly basic.
If I was talking with someone who challenged me to prove the existence of the Godhead I would appeal to three Arguments.
1. Argument from Contingency
2. Transcendental Argument
3. Above all the testimony of personal experience.
I think it's pretty obvious the Divine Exits. It only takes a little logic and reasoning to come to the conclusion that this Divinity is closest to the Wiccan conception of it.
3. If your tradition contradicts the tradition of another Wiccan, can they both be objectively true?
The thing is that some Wiccans believe that there is no set belief or principles that make one Wiccan. Some believe that you can pretty much believe whatever you want and still call yourself a Wiccan. I'm one of those new breed of serious Wiccans who understand that there are certain things that you must believe in order for you to actually be a Wiccan.
The only thing that a Wiccan must believe is that there is both a Goddess and a God who really exist. Other than this we can have disagreement.
4. How do you feel about believing in the religious system where you cater your religion to your desires?
This is a gross mis-characterization. Wicca is a religion with one core belief. As Wiccans we can have healthy debate and disagreement amongst ourselves on various concepts and beliefs. We do not cater to our whims. If we add an element that helps our spiritual practice that is not "catering" to our desires.
5. if you cater/construct your religion according to our desires, then isn't it nothing more than your own invention?
I reject that notion that we craft our religion to our desires, therefore this question is nonsensical.
6. Is Wicca able to be shown to be false or is it all non-verifiable ideas?
Wicca rests on three foundations that can be falsified.
1. The Divine, a separate realm of existence both a part off and separate from our material world exists.
2. There is a spiritual force that pervades this world and through it we commune with the Godhead
3. The Universe is fundamentally interconnected at an Atomic Level.
If any of these three propositions can be proven false then Wicca is false.
7. If your spells and incantations produce results, how do you know that the power behind the results is good or not?
Assuming that the Wiccan Conception of what allows magic to take place is true, then the notions of "Good and bad mean nothing to this because it isn't personal. The only way the questioning of the morality of the magical force could be asked is if the Christian pre-supposition that Demons are the source of magic is placed at the forefront. Needless to say I, and all Wiccans, reject that notion out of hand.
8. How do you know that there is not something more sinister behind Wicca?
This question is simply ill founded. The question can easily be turned around to ask, "How do you know Satan isn't responsible for Christianity." Think about it for a moment. Assuming the Trinity is polytheism, more at home in Wicca than in Monotheism, wouldn't the huge numbers of Christians around the world have made Satan's mission a success?
9. Why do you think that rituals dealing with candles, knives, and such are able to affect nature?
Because human Evolution has allowed our conscious minds to be able to affect our environment. An Aspect of Wicca is the eminence of the godhead in the world. Magic is the projection and focusing of the will through the Godhead in order to affect the world around us. It's more of a hyper form of prayer or a self-focus then it is some ultimate solution to life's problems.
There you have it. All of CARM's questions answered. Maybe they'll come up with new ones soon.