There is a potentially infinite data set. Just like the coin flip situation. There is no difference. You can flip the coin 350 times , and if the results are 52% heads, then that abnormal result may or may not be statistically significant, meaning it may or may not be sufficient to tell us there is some flaw in the coin causing it to land on heads.
Yes, that is exactly what we're asking. Whether this is a large enough sample of a potentially infinite data set to tell us whether the results here are statistically significant.
Maybe. Maybe not. Obviously there should be some influence. The influence may actually be greater than the stats shown here. I don't think the sample is large enough to really make any meaningful determination one way or the other.