Factor analysis and Cronbach's alpha My research work is based on a questionnaire which includes all types of questions, ordinal as well as nominal, but 80% of the questions are based on Likert scale 1-5. My question is whether Cronbach's alpha can be calculated for all types of questions even if they are not on scale format? Secondly whether  Cronbach's alpha or reliability should be done before or after conducting factor analysis and what if it comes to be too low? Also, how do we select questions from the questionnaire for factor analysis, can it be random?
 A: As mentioned in the comments by @ttnphs, Cronbach's alpha $\alpha$ is not appropriate for ordinal and nominal data, as it was designed for scale (or metrical data). Factor analysis, however, can easily accommodate ordinal and nominal data. When using factor analysis omega, $\omega$ is typically used as a measure of internal consistency. Unlike $\alpha$, $\omega$ is a model-based reliability estimate. Thus, it can only be calculated after the factor analysis has been run (and is returned by default in many software packages) regardless of your item type (just make sure the appropriate link function is used for each item).
I am not sure what you mean by item selection; if you could elaborate on the context, I may be able to help.
Below are a few helpful articles regarding the use of $\alpha$ in scenarios where factor analysis is the appropriate measurement model.
References
McNeish, D. (2018). Thanks coefficient alpha, we'll take it from here. Psychological methods, 23(3), 412.
Raykov, T., & Marcoulides, G. A. (2019). Thanks coefficient alpha, we still need you!. Educational and psychological measurement, 79(1), 200-210.
A: Before conducting factor analysis you need to perform the KMO test or Bartlett's test of sphericity to check whether your data is suitable for factor analysis.
You need to perform Cronbach's alpha test after the factor analysis.
If you want to know how to select the items please follow this link (I find it very helpful)
https://www.promptcloud.com/blog/exploratory-factor-analysis-in-r/
