1. Is this expected behaviour considering my design?
When you choose an "automatic gateway" option then your VBR picks up one on your proxies on site "A" as a gateway. The proxy server on site "B" has an access to you share, however, an "automatic choice" option prefers some other server as a gateway, which apparently does not see the B-share. The best approach is to choose the server that is the closest to your CIFS share.
2. When I kick off a backup job in Site B, the traffic always seems to travel through the Proxy that is set as the Gateway Server, is that normal?
Absolutely. That's the way it is supposed to work - gateway server is responsible for data processing as it is not possible to deploy Veeam Data Mover services on a CIFS share. Please see the link
3. When I start a backup job in Site A, the traffic seems to travel through one specific Proxy, even though Gateway selection is set to Automatic, is that expected?
Yes. Such behaviour means that "specific proxy" has been chosen automatically as a gateway to process backup dataflow. May I ask you - what did you expect an "automatic gateway selection" option would do? =)
4. Should I do anything different for the configuration of Site B, e.g. should I use a second Veeam Backup Server etc., or is the configuration I am using considered acceptable (best practice)?
At first glance, your configuration seems to be solid. Do you have any concerns about that?