On ETH01 assign IP 192.168.0.1/255.255.255.0 and enable DHCP server for that range.
On ETH00 you already have the public IP address. Enable NAT on interface ETH00. No bridging. No need for a static route, the Default Gateway is fine. Add a DNS server, maybe this could be a reason for not having internet. You can either use your ISP’s servers or OpenDNS.