Hello again,
the guess with Inventory Service seems wrong, I deleted the IS database as described and re-registered vCenter, this time with success, but the web client still barks at startup "Could not connect to...(endless list of old vCenter URLs). Then I looked into the SSO service output (ssolscli.cmd listServices) and found that there are some duplicates, and also my obsolete entries with the wrong FQDN...
Also the new installation ist listed there multiple times, even web client etc... seems not so clean Db anymore 
Is there a way to delete a service from there ?
2nd issue is resolved, which made us very happy: If you reconnect a host the VMs will not get thrown out of their folders. The wizard, not being very specific there, tells me to select a folder for the VMs of the reconnected host. But, if a VM is already known to vCenter, it does not move it to this folder. It seems to be a folder default for unknown VMs on this host (maybe during vCenter was down).
I think this should be made more clear inside this wizard page. It frightened us and led us to making a complete list of folder contents
regards Florian