You can use the factorial analysis method to validate or adapt the questions of an online survey to obtain evidence of validity and reliability under a theoretical framework. The analyses based on the SEM methodology propose the evaluation of latent variables (not observable) related to the social sciences. business, health, education.
Regarding the statistical method suitable a cross-sectional study, if you mean the variables among the study, thus they are in most cases related to corelation and association between 2 or more variables or variable in relation to outcome; there for i guess the most suitable are cross tabulation and multilinear regression tests. Noted that you might use chi square test for the cross tabulation and in case of borderline P value or in case where input variables of low number, then its better to use fisher exact test.
Mohanad Kamaleldin Mahmoud Ibrahim , thank you for your answer, I rellay appreciate you taking the time to answer my question. I dont need a method for analyzing the relationship betwee the predictors and the outcome/respone variable, however Im looking for the most optimal way to evaluate the representativeness of the datacollection. My data are independent and non-parametric.