VM action when host is shutdown

We have a 2 nodes Hyper-V cluster.

Failover VM setting "Cluster-controlled offline action" is Save

Hyper-V VM setting "Automatic Stop Action" is Shutdown

1) What happens if a shutdown a host ?? Will VM move to other host ??

2) What happens if a move a VM (domain controller) to other host ?? Is supported live migration on DC without shutdown computer ??