I would reccommend ou use Meta-XL in this case.

MetaXL will allow you to pool prevalence, as well as weighting by study size. You can also score the study quality and use the quality score in your weighting. This will also create an output of a forest plot. This is a free Excel add on.

I assume STATA calculates a mean of prevalences which will generally give a different value to a pooled prevalence

Try to calculate the mean of the prevalences in the various studies, rather than the pooled prevalence.

I agree with Muhammad, if you enter the studies individually they will each be given a different weighting and therefore produce a different result than simply entering the overall prevalence. The variation in study size and heterogeneity of results then produces the confidence intervals.

Both results should be different. One is not weighted (first, only dividing cases/population), compared to weighted pool prevalence. See this article: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.863.8189&rep=rep1&type=pdf

It depends first on your meta-analysis model (fixed-effect or random?), second on how studies are weighted. I guess you chose à fixed-effect model. Regards PG

First, decide which model (random or fixed) better fit with your data for meta-analysis. Otherwise, you will get a wrong estimate.

It depends on the model(either fixed or random) you are following. I think you will get more information from this article. Meta-analysis of prevalence (doi=10.1.1.863.8189&rep=rep1&type=pdf )