Proxmox should really be zone-agnostic here, so you're able to create VMs across multiple zones as needed, I don't think that's the issue.
You can use Proxmox's Network Tab to setup the 3 zones by either creating 3 separate interfaces and hooking them to each VM/LXC, or bridging the zones across a single one.
As for the applications, just check the logs for each service and it should tell you what's wrong.
Within the respective container, run telnet localhost [Port Number] - If it can't connect, then no web server is running and that's the problem. If you get an "empty" response, then it connected successfully. This can also be done as long as you're within the same network and firewall policies are properly configured. Umbrel gives you SSH access to its system, so may be easier to start there.