Cronbach's $\alpha$ - two instances From a survey I have the following data:
44 questions are supposed to measure 11 variables (underlying theory, 4 questions per variable). These 11 variables are supposed to fit into two categories (underlying theory, 5 variables category A, 6 variables category B). I am unsure how to test this. I was advised to use Cronbach's $\alpha$ instead of conducting a factor analysis, I have some doubts though.
Further I may have a situation like this: I use Cronbach's $\alpha$ and find let's say the reliability of the scales is the highest if always 3 questions are used for each of the 11 variables. Out of these 33 questions I create the 11 variables. And now the bit that confuses me (even more): To determine the reliability of the categorization, shall I test $\alpha$ of the 5/6 variables, or the 15/18 questions? Or would it be the same?

I am quite open to other approaches. I was thinking about looking into McDonald's $\omega_{h}$ or other FA approaches.
 A: It's important to make a distinction between two concepts here, one is reliability and the other is the internal structure of your survey (what you refer to as categorization). It seems to me that when you talk about "reliability of the categorization", what you actually want to get at is the internal structure of the test. More specifically, you want to know if there are really two factors underlying the 11 scales of your survey. And as far as I am concerned, by far the best way to do this is by doing a confirmatory factor analysis. 
In the comments some concerns have been voiced about the sample size. I am not a specialist in this regard and from all that I have read about CFA so far, this is one of the areas that are still a bit mysterious to me. However, a useful ressource that I keep stumbling upon is the website of David A. Kenny. He lists a couple of rules of thumb. Ratio of the sample size to number of free parameters in the model should be about 5 to 1, and generally 200 is seen as a goal. Depending on the model that you specify this might work out for you. If it doesn't, conducting two separate analyses for the two categories (or two factors) might help. I would definitely not be as pessimistic about your sample size as the commenters.
As I have said in response to another one of your questions, Cronbach's $\alpha$ should not be used to assess the internal structure (Sijtsma, 2009). It will be a lower bound to the reliability of your survey, but only when you have a $\tau$-parallel measurement model in the sense of Classical Test Theory. This is something you can find out by doing CFA. But I have the feeling that's not what you want, anyway.
References:

Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach’s alpha. Psychometrika, 74(1), 107-120.

