Unrestricted Climb
The aircraft was a departure, stopped at 5 on the SID. Probably had the sigmet, either on the ATIS or from tower about the icing. When he got stopped at 5, he did the prudent thing and asked for a higher altitude, unrestricted climb essentially informs departure that the request is not just for the view. Nothing to be read into this request as far as the icing conditions above. Done it many times
Altitude Readbacks
Not required in the US. However if you bust an altitude then the readback really changes things. If you read it back and ATC missed the mistake, then they can wear it. If you didn't read it back, and bust the altitude, then you're on your own