The cruel irony is that my roommate is a physicist.
My relatives are fundamentalist Christians. Not seeing the irony here.
The Big Bang
1) How did matter exist before the Big Bang so as to start it?
2) How did the matter have some kind of motion to start the Big Bang if time did not yet exist?
a) If time is infinite, how is there a present?
1) The current theory doesn't postulate what happened before the Big Bang. I don't think it argues that matter 'started' the big bang either, so to speak.
2) I'm not sure exactly what you're asking on this one, but the reason why the universe expanded rapidly is because of fundamental forces.
Also, time is definitely not infinite. The age of the universe is estimated to be 13.82 billion years, which is clearly finite. If you're talking about time being infinitely divisible, it's not. As far as we know, Planck time is pretty much the smallest unit of meaningful time.
Evolution/Origin of Life
1) It has been proven that amino acids could arise from conditions on the early earth, but the probability of RNA and other cellular structures forming is incredibly small.
2) When an organism develops a new organ, it will be a long, slow process. Each mutation must take the organ in the correct direction for it to eventually function properly in a beneficial manner. During the evolution of this new organ, the developing organ does not provide any advantage to the creature (in fact, a half-baked organ could be viewed as a disadvantage) and thus natural selection would not help in its development.
3) Why have we not observed any cases of evolution on a scale larger than microevolution? Shouldn't we be seeing some branch of a species in a transitional stage?
1) When you have a self-replicating structure, only the mutations/variations that are meaningful get passed on. Creationists often drop this ridiculous argument where they compare the human genome to a slot machine, but that's not how it works. The 'useless' combinations of genes are avoided by natural selection.
2) That's not even true. There's fossils and living organisms that have primordial forms of eyes. Unsurprisingly, these rudimentary eye-like structures are advantageous, since they exist in populations. For example, the nautilus.
The whole 'evolution of the eye' creationism argument has been addressed by scientists for decades.
https://en.wikipedia.org/wiki/Evolution_of_the_eye3) You don't see evolution progress in real-time because it's an incredibly slow process. There are no such things as 'transitional organisms', so you don't see those either.
Creationism
1) God is not observable.
Definitely not observable. If you live your life trying to find conclusive evidence for his existence, you'll leave disappointed.