I say this in the nicest way possible: it looks to me like you're in over your head. I'd recommend getting your hands on a classical test theory textbook like Crocker and Algina.
For the Mean, you're not looking for the mean frequency. You're looking for the mean total score for people who selected that option.
Step 1: score each response against the key
Step 2: calculate total score for each candidate
Step 3: find the sum of total scores for candidates who selected the option
Step 4: divide that sum by the number of candidates who selected the option
Hope that helps.
Edit to add: you can't calculate a standard deviation for a single score.
>you refute 70 years of personality research
There wasn't ever extensive validation of the Big Five. Denny is also not a fan of the Big Five.
>one of the best sources on validity in our generation (Borsboom)
I am stating the same thing Borsboom believes with regards to validity: there has to be evidence of the construct in question causing response variation. This obviously requires structural fidelity because if the underlying factors do not provide evidence for the construct theorised about, it won't be the thing driving response variation. If you read Borsboom's thoughts on validity, you'll walk away understanding this. How you think I said something that contradicted Borsboom, I'm not sure. And Borsboom is clear about how this idea is not original to him too. It was stated by Cronbach almost 70 years ago and pretty basic textbooks say it too. Here's an example:
>[T]he construct must be defined in terms of its logical or mathematical relationship to other constructs within the theoretical system.... If such relationships cannot be empirically demonstrated, the measurements obtained are of no value.
There are many sibling studies, and some common pathway models for personality, in addition to lots of studies finding cross-cultural failures of MI.