Is the Cosmological Argument irrefutable?
Refutability is in the eye of the beholder! Here is the Kalaam Cosmological Argument:
Premise: All things that begin to exist are caused.
Premise: The universe began to exist.
Conclusion: The universe was caused by a Creator
Some people may not accept the first premise. I have never heard a single proposed example of a thing which began (the key word is began) to exist which was not caused, but some will challenge this premise.
The second premise, is, for all practical purposes, irrefutable (Although some do debate this premise and continue to push the theory of continuous creation. These people are a dying breed, literally)
If the first two premises are irrefutable, then the argument is irrefutable. Of course, some people do not refute either premise, but choose to ignore the implication anyway, because human beings are not as logical as some of us like to think.
On your second question, we simply do not have a date for the flood. Given that the last ice age ended about 20,000 years ago, I think that most who would try to estimate the timing of the flood would put it after the last ice age, but there is no absolutely certain way to date the flood, in my opinion. Sorry to have such a non-answer, but it is the best I can do.