Test-retest sample size, factor analysis and cluster analysis


I am developing psychometric questionnaire to assess project manager competencies in the region (which they actualy have - not state they do). I`ve backed up my questions with some previous research - there is about 140 competencies grouped in 8 "blocks" (individuality excluded). I`ve grouped them and generalized into 43 statements (situational, behavioral and tricky - to avoid self-exaggeration) with Likerts scale from 1 to 5 (strongly disagree to strongly agree).

1. What is an appropriate/minimum sample size for test-retest reliability in the pilot research if the main sample is going to be aprx. 300?

2. Is it possible to carry out EFA to check those 8 blocks with 300 sample size and 43 variables?

3. Is the cluster analysis is a proper way to check the competencies differences based on managers experience in whether public or private sectors?

I would be grateful for your help.