AFAIK, the Network and Sharing Center settings in Vista has nothing to do with third party firewall but all settings applies to Windows Firewall in Vista.
If you have Windows Firewall only, you can attain your goal. However, if you prefer to use third party firewall (Comodo or others) while Windows Firewall is disabled (disabled by third party firewall or by you), the said settings for that 2 items will be enabled automatically. It is why Network and Sharing Center says:
To turn off network discovery, Windows Firewall will be enabled
To turn off file sharing, Windows Firewall will be enabled
As to your question on how to enable private networking in Comodo... you've already enabled it, if you did not 'check' the box for "I would like to be fully accessible to other PCs in this network" which is one of the option when you saw the dialog box that says "New Private Network Detected" and that prompted you to give a name.
Before I had installed Comodo. I had enabled Private Network and disabled Network Discovery and File Sharing in the windows firewall...
But after I installed Comodo, I find that Network sharing and File Sharing is switched on even though its shown as private network under the network and sharing center...
When I installed Comodo a dialog box appeared saying that it had found out a private network and what name I would give. I gave the name and clicked ok...
How do I enable private networking in Comodo? I don't want to share anything at all.