The letters used to be pronounced, and they did not update the spelling to keep up with the changing pronunciation.
Similar to English -gh in "through" or "though", for example, which used to be pronounced (compare the related German durch and doch, where the ch is still pronounced) and is now silent but is still written.
You are correct. The g's are often "soft" like you say. It also makes the i longer as opposed to the word "pi" (the mathematical constant) which has a very short "i" sound. So short, in fact, that it's hard for foreigners to learn to say, but that's a different story about short Danish vowels.
It is just a different language. "Slut" also means something inoffensive :D