Hi, Nucleus uses the ports below:
3009: API
3030: Large File Transfer Service (LFT) port
3100: Authentication service port
3180: Authentication login port
3333: Discovery Service port
3080 and 3085 is being used by the Omniverse System Monitor
Looks like LFT service fails to start. Try stopping all Nucleus service and make sure port 3007 and 3030 is not used locally and try installing again.
Yes, this is the default outbound rules for a security group.
In the inbound rules, do something similar but with your public IP address to allow all traffic to that IP address.
IPv4 All traffic All All <public_ip_address>/32
Note: Having a static/non-shared public IP as well as a VPN is recommended for a secured connection.