You have to be an admin to make firewall changes. AFAIK there is no explicit permission that can be granted to allow changing firewall settings.
What I don't understand is why you would need to do this anyway. I don't play Minecraft so I'm unsure how mods impact it but presumably they are just DLLs that load into the process memory.
Firewall rules are defined by the EXE. If you allow Minecraft (the EXE) through the firewall then it is allowed. It doesn't matter what it tries to do after that. If a mod tried to run its own EXE then a firewall rule would be necessary.
However that is a good thing because you wouldn't want your son to download a malicious mod that silently uploads all his personal data to a site. That is the whole purpose of using firewalls.
If you need more granular control over the firewall then search for "Windows Firewall with Advanced Security". This app gives you more control over what is allowed. The default firewall UX allows you to allow/deny a program on various network profiles. The advanced version allows you more flexibility such as allowing specific ports and whatnot.