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if I copy a spell with chandra for example and I have guttersnipe out will my opponent take 4 damage?

No. The copy wasn't cast, so Guttersnipe 's ability won't trigge from it.

Only if the copy effect tells you to cast it. Chandra, the Firebrand does not let you cast the copy (it gets created on the stack directly). Isochron Scepter does let you cast it.

What about cipher?

Cipher casts the copies