P-value calculator
A p-value is the probability of seeing data at least this extreme if the null hypothesis were true. It is not the probability that the null hypothesis is true, it is not the probability your result is a fluke, and 0.049 is not meaningfully different from 0.051. The threshold of 0.05 is a convention Fisher suggested casually in 1925, and the replication crisis of the last decade is in large part a story about treating it as a bright line.
Assumes a normal (z) distribution. For small samples you need a t-distribution, which has heavier tails and gives larger p-values for the same statistic.
A p-value is the probability of a result at least this extreme under the null hypothesis. A z-score of 1.96 gives a two-tailed p of 0.05, which is why 1.96 is the critical value everyone quotes for a 95% confidence level.
How to find a p-value
Choosing one-tailed after seeing which direction the data went is a well-documented way to halve a p-value without doing any additional work, and it is not legitimate. The tail choice belongs to the hypothesis, decided before collection: a one-tailed test says you would treat an effect in the opposite direction as no more interesting than no effect at all, which is rarely true. When in doubt, two-tailed is the conservative and defensible choice.
Questions
Conventionally below 0.05, but that threshold is a convention rather than a law. Report the actual value.