(Perhaps this would be better as a comment, but I can't comment)
I don't understand why you're asking this question before you've watched all the episodes. Is this the first time you've seen something unexplained on a TV series? Typically, it's explained in a later episode.
If you insist on being spoiled, read on. Be warned though that I'm including as many spoilers as I need to to explain it adequately.
Regarding the song existing in that universe:
When the Galactica people reach Earth, the four begin to remember things from their lives on it. Anders in particular remembers that he used to play this song for the rest of them.
Given that the entire thing happens in the past of our history (within the fictional universe), Bob Dylan (and not Led Zeppelin, or Jimi Hendrix) didn't come up with the song. The words of a song from thousands of years before his time just came to him. How that happend is possibly explained in the next tag.
Regarding how the four heard the song and how it made them realise they're Cylons:
God did it.
As far as I can tell, that's the intended explanation, as no better one is ever given.
Baltar, Caprica Six and others are eventually convinced that the Cylon God does exist and affects how things happen. So the best explanation for anything left unexplained is... God did it.
