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Religion
Physics

During a conversation with my friend about cosmological argument for God, friend told me that cosmological argument is not even true because causal principle is outdated and not needed in modern physics. After the conversation, I searched for that by internet and found out Russell first argued like that and many contemporary philosopher of physics agreed that causality is at least not needed in our fundamental physics. I think if this kinds of argument succeed, then causal principle is undermined and as a result cosmological argument cannot be hold. So my question is, how do proponents of causal principle and cosmological argument answer to that?

I could be wrong, but I believe that few philosophers today would claim that causation (per se) can be eliminated in an adequate description and explanation of the world. Indeed, it would be hard to understand our communicating right now (my intentionally responding to you, using computational mechanisms) without making use of cause-effect relations. There are abundant philosophical treatments of causation ranging from those that appeal to laws of nature, counterfactuals, Humean regularities.... I myself favor the idea that causation is best not understood as fundamentally involving laws of nature; I suggest that what we think of as laws of nature are abstractions that rest on substances (things / particles) that have primitive or basic causal powers and liabilities, but this (like so many things in philosophy) is controversial. There are still defenders of the cosmological argument for theism. You might look at what I think is the excellent entry on the cosmological argument in the free online...
Physics

Is it conceivable that something finite can become infinite? Isn't there an inherent conceptual problem in a transition from finiteness to infinity? (My question comes from science, but the scientists don't seem to bother to explain this, such as in the case of gravity within a black hole -- a massive star collapses into a black hole and gravity in it rises to infinity? The more interesting example to me is the notion that the universe may well be infinite, but the main view in cosmology is that it began as finite and even had a definable size early on in its expansion. How could an expanding universe at some point cross over to have infinite dimensions?)

Good question, and a controversial topic! Some philosophers, going back to Aristotle, are happy with the concept of a potential infinite: a series that expands indefinitely. But they are unhappy with the concept of an actual infinite, partly due to the supposition that an actual infinitude could never be attained through any number of succesive events / acts. Start now, and no matter how many events transpire it seems that (just as there is no greatest possible number) you would never reach infinity. There are abundant puzzles, going back to Zeno in the fifth century BCE, about achieving an actual infinite. Here are two brief ones, the first is called Hilbert's hotel. Imagine (for the sake of argument) that you have an infinite number of rooms in a hotel and each person pays you $50 per night. How much money do you bring in per day? An infinite amount. But now imagine guests in rooms divisible by 1,000 all check out (guest in room 1,000 checks out, guest in 2,000 check out...). How much less...