Is something skipped here? Like "(when) the stars (start) exploding"? Can I skip like this even in daily conversation? Would if sound weird if I skip like this?
Yes, the speaker means "and (when) the stars (start/are) exploding." It is common to omit words from lyrics like in this song, but we do not do this in daily conversation or normal speech. It would sound confusing and inaccurate to omit words like this outside of the musical context.
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