1. Those were regional cooling and warming trends associated with North Atlantic circulation patterns, not global climate change.
2. This is incorrect. CMIP3 and CMIP5 Global Circulation Model ensembles accurately predict observed warming trends when aerosol forcing events, specifically the 1981 El Chichón and 1991 Pinatubo eruptions, are included.
3. What do you mean? There are hindcasts of past climate scenarios. But you cannot run GCMs "backwards" any more than you can run aerodynamic models of turbulent airflow over aircraft wings backwards.
4. They include water vapour, aerosols, solar output, parameterized clouds, and ocean currents. UHI effects are removed from surface temperature records by homogenization methods and do not play a role in large-scale climate models.
5. Raw data and software code are freely available. That 'skeptics' have done nothing with this reflects their own lack of ability or real interest in doing so, not a lack of data to work with.