To answer your question about distributed switch and traffic flows, there is nothing special about how a distributed switch moves packets compared to a standard switch. The vDS exists to simplify management as it's a control-plane object; not a data plane object. Just like a vSS, you assign one or more uplinks to a vDS. Those uplinks are in a profile and this profile will be applied to any host belonging to the vDS. And just like a vSS, the virtual machine port groups use those uplinks to ingress/egress their traffic. How that happens depends on the teaming policy applied to the vDS. With a vDS, there are many more teaming policies available compared to a vSS, but those teaming policies don't determine how traffic reaches other hosts on the vDS, it determines how traffic leaves each host. Where that traffic gets switched or routed is irrelevant to either the ESXi host or the vDS object; that's a concern for external networking infrastructure.
Lastly, regarding DHCP, I would just add that if you're using Veeam for failover, it has the ability to re-IP VMs as well as assign the replicas to a different destination network. These two things in tandem give you just about whatever you need to have a given VM get the necessary network services on the destination side.