From my understanding, glm(not glmer) and GEE both handle binary values. But GEE is a marginal model and glmer is a random effects model (mixed model). So then what is the main difference between GLM (Not glmer) and GEE? Is GEE a longitudinal data version of GLM? Does it mean you can run 'glm' to only cross-sectional data?
Indeed, GLMs do not account for correlations you may have in your outcome data. Hence, they are more suitable for cross-sectional data, because in longitudinal data you expect that measurements over time from the same subject are correlated.
With regard to the interpretation of the coefficients you obtain, the GEEs can be seen as the equivalent of GLMs because they will also have a marginal intepretation. This is different than generalized linear mixed models, in which the fixed effects coefficients have an interpretation conditional on the random effects (though based on recent developments it is possible to get coefficients with a marginal intepretation from a GLMM; for more info check here).
With regard to the estimation, as mentioned in one of the comments above, GEEs are not based on a model that has a specific likelihood. On the one hand this makes them semi-parametric and you do not need to specify the distribution of your data, but on the other hand (i) you can only use Wald tests and not likelihood ratio tests, (ii) they are less efficient than a likelihood-based model in which you have appropriately specified the correlation structure, and (iii) in their basic form and with regard to missing data, they are only valid under the missing completely at random missing data mechanism, whereas a likelihood-based approach under the missing at random mechanism.