You can find standard error by taking the standard deviation divided by the square root of the sample size.
Critical values determine whether or not to reject the null hypothesis. If you have an observed test statistic (calculated from a formula) that exceeds a critical value from a table, then you have to reject the null hypothesis and accept the alternative hypothesis. If the observed test statistic does not exceed the critical value from a table, then you fail to reject the null hypothesis. For example, how do you translate a significance level of 0.05 into a critical value? It depends on the type of test you are doing. For a one-tailed test, you don't split the value. For a two-tailed test, you split the 0.05 into 0.025 and 0.025 for both tails of the distribution curve (a two-tailed test is like a confidence interval in that respect). If you use a z-table for a one-tailed test at 0.05 level of significance (meaning the alternative hypothesis is showing a specific direction like "less than" or "greater than" in its statement), then you will have a critical value of z = -1.645 or it could be z = 1.645, depending on the direction. This will determine where you "draw the line" to reject the null hypothesis. If you use a z-table for a two-tailed test at 0.05 level of significance (meaning the alternative hypothesis is showing no specific direction and uses "does not equal" in its statement), then you will have a critical value of z = + or - 1.96 (meaning either tail of the distribution curve). For example, if you had a test result of z = +2.00, then you would have exceeded the positive critical value of +1.96 for this particular test result and the null hypothesis would be rejected in favor of the alternative hypothesis.
I hope this will help.