Ruby minor version update and gem versions

Regarding Ruby version updates and gem versions:

  1. If I upgrade from Ruby 2.0.0-p247 (using rbenv) to 2.0.0-p353 do I
    have to re-download all my gems? What about upgrading from 2.0 to 2.1?

  2. If I use rubygems-mirror to create a local mirror can it be updated?