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I will assume that your questionnaire is to be considered as one unidimensional scale (otherwise, Cronbach's alpha doesn't make very much sense).It is worth running an exploratory factor analysis to check for that.This validity comes in different forms, all relying on the method used for the validation procedure.Depending on the specific situation for the questionnaire, the creators may choose to use one or many of the various validation methods.You can also assess convergent and discriminant validity by using Multi-trait scaling or Multi-trait multi-method modeling (based on interitem correlations within and between scales), or, again, SEMs.Then, I would say that Item Response Theory would not help that much unless you are interested in shortening your questionnaire, filtering out some items that show differential item functioning, or use your test in some kind of a computer adaptive test. For polytomous ordered items, the most commonly used models are : Only the latter two are from the Rasch family, and they basically use an adjacent odds formulation, with the idea that subject has to "pass" several thresholds to endorse a given response category.Face validation may well be the simplest form of validation.For this method of validation, no quantitative methods are needed.
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Content validation refers to observing all the specific items on the questionnaire to determine whether the questionnaire addresses the topic overall.
This type of validation is often the most important validation in developing new questionnaires.