Initially I could only access the first website with Filezilla over SFTP-SSH. After I changed the owners of web2 and web3 to web1:client1, I could also access these sites with the same username as defined for web1.
This was a bad idea as you broke the ispconfig system with that. Every website ahs its own user. You shoiuld undo that.
To your other questions:
1) Because every server that is connected to the internet needs a fully qualified hostname. Otherwise other servers can not lookup its hostname.
2) Most likely because you broke the system with your changes.
3) This is not a file from ispconfig nor used by ispconfig. ispconfig configures webalizer on the commandline and creates the stats for the domains based on the vhost logfiles. The /etc/webalizer file is most likely from your linux distribution and should be disabled.