Bringing in iphone 8 for a repair!

It the back of the iPhone is also damaged (I'm assuming the glass is also cracked, your only option is to do a service replacement unit, Apple does not repair the back glass as it is fused to the frame.

iPhone repairs can be performed at either the Apple Store or an Apple Authorized Service Provider. However, the technician may have to extend the repair period if other damage is found outside of just the screen itself. Regardless, if you have an active AppleCare+ plan on this phone, any repairs will come at a reduced cost. Depending on the damage found, they may not be able to fix this phone. In such a case, they would offer a replacement ... again, at a reduced cost.

Your cost will be $99 plus applicable taxes: iPhone Repair - Official Apple Support

No I don't but if you purchased AppleCare + in the UK it should still be valid in Norway.