Undergraduate Master degree vs first get a BSc and then Postgraduate Master

I've heard people saying that if you apply for an undergraduate Master degree you will get MEng or MSci, and first doing BSc and then apply for postgraduate Master degree will get you a MSc.

Personally, I'm very interested in the specialisation of Artificial Intelligence inside the Computer Science master degree, so my questions are:

1. Is MSc at advantage when compared to MEng or MSci for oversea jobs in the US or Europe?
2. Is MSc more expensive than an undergraduate master degree? I've heard graduates have to fund themselves to do a postgraduate degree and will receive no help at all from the university.
3. Which route would you recommend?
4. Which is better for applying Phd?
5. What is the main difference in the structure in the programme or assessment? (if any)
6. Will too much specialisation in AI be bad for finding a job after you graduate?
7. Is it true that you can graduate BSc from 1 university and you can apply for MSc elsewhere?