well, I didn't find any issue from your work, and you have some basic routing and switch problems. I will try to make it simple...
nat isn't for routing, nat is to prevent private networks to expose on public internet which cannot route private address, and nat is used to allow private networks to access public internet.
port forwarding is used to provide private services to public networks.
vlan is used for separate networks, vlan can't communicate with other vlan directly, they communicate by routing.
so, in your work, nat is used on wan port which replaces source (private network address) to public address, then the public address know how to transmit back.
port forwarding is like someone access your public address port 80, which is HTTP, then your firewall forward the request to the server in your private network
in your private network, your firewall performs like a router, who knows every network, so if an address from LAN want to access an address in SERV, then it will forward the packet to the gateway of the LAN, which is your firewall LAN address, then the firewall know where next-hop is, it will forward the packet to SERV network.