"...I was just thinking about why I'm Jewish. I mean, if someone were to ask me, I wouldn't know what to answer...the answer that came automatically to my mind was, 'well because I was born Jewish.' But that's not really an answer because my birth religion can be understood as a kind of accident, couldn't it?
"I know God is one, infinite, we are His chosen people, the Torah is true, but is that why I'm Jewish? Do i fully believe that or am I just saying it because it's been told to me so many times? How would I prove all this to someone else? Or even to myself? Should I take one of those Aish HaTorah outreach seminars?"
I don't believe that anyone is born with an automatic reservoir of faith - no matter who his parents are. With that in mind, when I teach my high school students, I make it a point to regularly raise these issues. I also encourage all questions. I want my students to have to face their relationship with God as mature people and not just go their whole lives happily but superficially keeping mitzvos. The superficial approach may work up to a point, but they'll surely miss most of the Torah's joy and substance...and if life should ever throw them a serious challenge, the results could be devastating. In short, I agree that your questions are reasonable, proper and among the most important you might ever ask.
So what's the answer? I believe that there are two types of faith: emunah peshuta ("simple" faith) and faith that's acquired through analysis. By emunah peshuta, I don't mean sitting all day with our tehilim (Psalms) just because "my father told me this is the way it is..." As you implied in your question, if that were all, it would make no qualitative difference if the believer was Jewish or Hindu and if the activity was reciting tehilim or practicing eastern meditation. Rather, emunah peshuta is that clear, intuitive knowledge of God that comes only to people raised since childhood in a pure, uncorrupted world, cut off from alien values and thoughts. I think that's what's meant by "and Jacob was a man of 'tam' ('simple')..." (Gen. 25; 27) - not that he was a simpleton, but that he was pure and uncorrupted (and I think that fits better with the Talmud's general use of the word tam).
Unfortunately, I would imagine that it's nearly impossible in our world to raise children with this kind of purity: even if you didn't grow up with a TV, the first time you saw some advertisement exalting this model car or that breakfast cereal as the answer to all of life's problems your values diverged from the Torah's. Deep down inside, you began to think that the consumer lifestyle is what's real and nothing else. "Who's really important? John F. Kennedy or Michael Jordan or the Beatles! How could I believe in God, scientists don't give Him much value, do they?" So God ends up taking a back seat in our consciousness.
Emunah peshuta, then, is a bit beyond our experience.
Emunah through analysis, the second class of faith, would therefore be the route for the rest of us. Now this analysis can take more than one form: For some people the very complexity and balance of the Torah itself testifies to its truth (perhaps a bit like the reaction a famous British mathematician had upon reading the calculations of an unknown and self-taught Indian post office clerk - "I honestly can't say that I fully understand what he's doing, but anything this complex has got to be true!"). Once in a while I pause in my learning and marvel at the completeness and perfection of Torah: no human could ever have made this up.
Others need a more immediate and rational style of analysis like that of the Kuzari. In our generation, I haven't seen anyone who's done a better job presenting and adapting the Kuzari's approach than Rabbi Dovid Gottlieb (of Ohr Someach - himself a former professor of analytic philosophy). If you're up to some intellectual stimulation, try the electronic version of his approach here.
Going to an Aish seminar isn't a bad idea, in fact, they and Ohr Someach are both developing versions for religious audiences. Some presentations are a bit heavy on "Bible codes" for my taste...but that's another discussion.
In a similar letter...
My 14-year-old son says that "God is a jerk" because He doesn't intervene to prevent little kids from being abducted and murdered. My son says he no longer believes in God because he has no use for a God who stands by and watches while horrible things happen to innocent people daily. He says that the standard response of "we can't understand God's ways" isn't good enough and is just a cop-out. What do you suggest...
I can certainly appreciate that your son isn't satisfied with simple admission of ignorance of the Divine plan. For one thing, this answer (while it certainly has a lot of truth to it) is really only appropriate after a person is comfortable with the concept of a personal and living God. But if your son is like the vast majority of kids his age (even many of those belonging to religious communities), then he probably hasn't yet formulated his own mature and intelligent belief. In other words, deep down inside, he might not yet even believe in God.
You should assess this yourself, but I suspect that it might be worthwhile discussing this issue with your son, perhaps encouraging him to think or read about the fundamental questions of faith for himself. Now, I'm sure that he's not yet ready to investigate Kant, Kierkegaard, Russel and various Aristotelian and Eastern philosophies of faith (nor will any of us likely live long enough to try it ourselves). But that doesn't mean that he can't talk about the God of the Torah and about how we can demonstrate evidence of His existence.
In answer to your son's question: the existence of evil in this world is only a philosophical problem if you can prove that this world is all there really is. But if your God controls His world, is just and kind, and sets all accounts straight in the next (through punishment and reward where appropriate), then drawing conclusions from the things that happen here (no matter how tragic and horrible) is really seeing only half of the story. Who's to know that the "pay-off" in the next world isn't many times greater than the suffering here? Don't people willingly suffer years of privation and pain on the hope of getting a dream house or car? Can we say for sure that God's next world is any less of a "dream" and less useful than those toys?