Cross sectional data is collected by observing many subjects (such as individuals, firms, countries, or regions) at the same point of time, or without regard to differences in time.
Formula to calculate sample size is given in following link:
https://communitymedicine4asses.wordpress.com/2014/05/11/sample-size-calculation-cross-sectional-studies/
There's no single answer because it depends on what question you are addressing and how you plan to examine the data.
In particular, what kind of effect(s) do you anticipate based on theory and prior work, as that would then lead to power estimates of what sample size you require to have meaningful power to detect a real effect.
Power will also depend on what kinds of analyses you plan to do, e.g., simple group comparisons will be less costly in terms of sample size than multivariate techniques such as multiple regression.
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