I think you are already aware that vmotion is not supported for virtual NGIPS/FTD. Theoretically it should work (RARP is sent after vMotion, so if you have a distributed portgroup with promiscuous mode active on both hosts traffic forwarding should work without issues) but no firewall vendors will support it since there could be traffic disruption due to vmotion.
To work around this limitation you could use HA. Bundle two virtual FTDs into an HA pair using FMC. If you only want to rely on infrastructure HA using vMotion you would have to calculate with downtime if your host is down. If the VM resides on a shared storage and the same portgroup is available on another host, it will work fine, rebooting on another host works.
Considering your third question... I dont think a reboot will be required but I will check that in my lab and get back to you. :)