re-install the operating system

Hello - you need to reinstall the OS and the application, and install Autostart rejoining it to the existing Autostart domain. However, in case you are using EMC Mirror data source on Windows, you will need a short downtime in order to recreate the Mirror data source (you need to delete and create again the data source and this requires the shutdown of the resource group). If you are using shared disk or RDF data source, this is not necessary and it is very likely that you will be able to establish the cluster again without downtime.

Yes, first add the node to the domain, verify that the configuration is ok as far as the nodes go, and the take offline the resource group, delete the mirror data source from the resource group configuration, delete the data source, and create it again. Since the valid data at this moment is on node B you will select node B as the source node.

Then add the data source to the resource group (make sure the position in the startup and shutdown sequence is correct), and that bring online the resource group on node B. At this point the data source should start the initial sync, and until it is completed it will stay in warning state but you should see the percentage progress mark.

Once it syncs you can do a failback again (if the application or service is configured properly on the reinstalled node).