Applying S1 visa in third country.

TravelChinaGuide,

I've heard that applying Chinese visa in third country requires that you have to have 6 month valid entry permit in the country where the application is being made, but the visa applied was tourist.
I reside and study in China and have the X1 type. My wife and son now want to apply S1 type so we can be together.

They have Somalian passport and they would apply the S1 in Djibouti since we don't have Chinese embassy in Somalia.

What I would like to know is:

1. Do we need 6 month stay permit in the country where we would apply the S1 type?
2. Does my wife and son need to be present at the time of the application at the embassy, if not, can I or another trusted person/agency submit the application?
3. How long would it take the process of the application?

Thankfully
Barre