"the standard error of the mean is usually estimated as the sample standard deviation divided by the square root of the sample size (assuming statistical independence of the values in the sample).
Yes it is possible to go back and forth from SD to SE to 95%CI. You can substract the mean from the upper 95%CI and divide the difference by 1.96 to find the SE. From here, you should be able to convert this number to the SD with the equations provided above. Traditionally the Effect Sizes are calculated with some form of the SD, so make sure you are using the correct terms. Have a second researcher come through and double-code and calculate these values independently. Then check your values versus theirs to make sure no calculation errors were accidentally made.