Seems that most of these questions have been already answered in this topic above... But still a few additions below.
1. While VPN is generally not required (though is a common practice when traffic goes over Internet in terms of security), you need to have servers involved in the backup process (remote hosts, backup repositories, and Veeam B&R console) see each other. In the product user guide you can find a list of all ports required for the backup.
2. Generally yes, but depends on the specific scenario you want to implement.
3. Depends on too many factors (the contents of the VM disks, in first place). Note that Veeam B&R also provides inline deduplication
, which together with compression allows to significantly save on transferred traffic and storage space.
4. You can use a single Veeam B&R server to backup all the VMs, but definitely need local proxy server installed in each remote site.
5. Pretty easy. You can always import the backup file to the newly installed Veeam B&R in the remote site and make it ready for restore. Otherwise, you can use a standalone utility (extract.exe) coming with every Veeam B&R installation and allowing to restore VMs from any VBK file, even without the product installed.