swiss passport holder going to study in Shanghai

Hi
I'm going to study in Shanghai the school starts on 12th of september and ends on 3th of march.
I want to travel to beijing first and then go direct to shanghai. But with the Invitation letter i got from the school i only can get a visa for 180 day's.
1. can i do a tourist visa for Beijing and then go to Hongkong to get the visa for Shanghai?
2. some ppl. Told me it's better if i go to korea to do the visa. Is that correct?
3. how long would i need to do the visa in korea?

Thanks Natascha