How to move data from my old hard disk to my new one?

That is a hardware error code, it could be the cable or the drive. Get an external case for your drive (some new/replacement MacBookAir drives can be purchased with an external case for the original drive) If it's not damage to the the dive it will mount (if it mounts you may need a new SATA cable for the MacBookAir). From the New OS install you should be able to use Migration assistant to transfer the files... OR use TimeCapsule to restore from your old backup.

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