1. You can link two iTunes accounts via the Cloud Family sharing option. Choose one phone to be the parent and one to be the child. You will be able to share iTunes purchases (movies, music, apps), contacts, calendar events and photostream. Doesn’t quite completely sync the phones/iTunes accounts, but is pretty close. I do this with my personal iPhone and my work iPhone.
2. No you don’t have to unlink the 5C. You can have more than one iPhone/device attached to the same iTunes account. You can attach your new phone to your iTunes email, it will then mirror your 5C (assuming its on the same iTunes account) then you can take your 5C off any time you like.