Hi,
I also work at NCOC and will be happy to help
1) Do you know who provides the best mobile broadband deal in the area, I'm looking for a high data usage / Unlimited 4G package I can sign up to quickly?
Kcell or Beeline -both are good and not expensive. You can pay around 1800 or 2500 KZT (around $8)/per month, but anyway NCOC will provide you the mobile phone
2) Does anyone know if Skype (or Skype like packages) work for calling uk in Kazakhstan?
Skype works in Kazakhstan, or even you can install it at work and use whenever you want