In Spanish, "Chefen" is "Los jefes". Strangely enough, the "j" in "Jefe" is almost pronounced the same as the "Ch" in "Chef", a bit like the scottish "ch" sound but softer. It was from this, that I discovered that both these words, in Spanish and Swedish, come from the same Latin root word which means "chief". You don't see Latin cognates often in Swedish, but when you do they are sure interesting!
Depends on where you go. The sound that Astrid (computer lady) uses is indigenous to southern Sweden, if I am informed correctly. Swedes from the north, and also possibly Fenno-Swedes (can someone verify this?), use the "sh" sound. This also applies to the "sj" dipthong, and "sk" before soft vowels (e, i, y, ä, ö). "Ch" also only shows up in foreign loanwards, like this one, which is French in origin.
Yes it varies a lot. It could be pronounced with a "chess" sound and the spanish "jefe" (can't think of english example). I would say you're mostly right about south/north. Although I can think of so many different ways this is pronounced in Sweden, focusing only on the REST of the word :'D