how did Sarah Connor know so much about Skynet and "the future"?
If you watch the first film, you'll see that
- she learned everything from Kyle Reese, who was sent back in time to protect her when the first terminator was sent back
- she made recordings to give to her son, to explain everything to him
In the second film,
- the Terminator sent back in time to protect John told Sara and John a lot of the history of Skynet. Much of this happens off camera, but is clearly alluded to when Sara asks the Terminator to tell her everything .
why doesn't anyone else know the things that Sarah Connor knew?
Again, in the first film,
- Reese tried to explain what was going on to the police, but their psychiatrist decided he was crazy and discounted the story.
If you watch the second film, you'll see that
- Sara tried to tell people about the problem, but was found to be clinically insane by the same psychiatrist, and her information ignored
Additionally, there is no evidence that anyone else was ever told about the future.