Hi, I am in Astana. I have not much idea of other cities in Kazakhstan. I would only like to tell you that you should better raise these issues with the HR/Recruiter of your company. They will be in the best position to guide you.
In General, I can answer your two questions. 1. If you have full pack of documents, it will generally take only 5 days to get a visa. This is the case with all Visas except Residence permit one.
2. Yes, you can bring your family members as dependent to Kazakhstan.