SSRS can be upgraded seperately to the latest version, I believe without upgrading the db engine, but SSRS cant be upgraded without the db engine running, as the upgrade will need to make changes to the Reportserver database.
Im not sure what you mean by "migrate off". SSRS requires a running db to work with.
Although another contributor had stated its not supported to run SSRS 2016 on SQL 2008, it may work. But just because its possible doesnt mean knowingly entering an unsupported config is a good idea. I'd only do it if i was desperate for an interim solution.