But the DNS could automatic change the A records,
Of course. But you will get requests to the old and new location for up to 48 hours then as dns records are cached by the dns servers of the internet access providers.
Thats the problem that Mark_NL alreyd pointed out in #3
applications like vmware vsphere can do it as they control the network level, so they do not switch a website to another server, they move the complete VM incl. the IP to another server. Thats quite easier as you dont have to change a dns record. This kind of moving around a setup can be done with openvz as well and might be supported in the ispconfig virtual server manager as well. But moving a single website without interruption is a much more difficult task.