I just disabled firewall on my router to allow updating an iPad. Is this adviseable ?

Hello.

I just disabled the firewall contained in the Airties modem-router supplied to me by my ISP (Orange): my first line of protection. I believe I needed to do that for the purpose of enabling iTunes to connect to the Apple servers and download the current (9.0.2) update to iOS for my iPad. Otherwise iTunes said internet was "Off" on my home network.

UPnP was enabled. In addition, I also enabled port transfer in UPnP. Checking with Shields Up of GRC, i just verified that UPnP was not discoverable from the WAN side.

Gatekeeper in "On" (in between).

Last the individual firewalls in the two macs are, have always been, disabled.

Since Disinfectant for mac OS 6 and 7, I have not used virus removal tools for ages.

Am I being prudent enough ?

What would be advisable for me to do ?

I don't think you need to disable the router's firewall to update any go those devices. I've updated a Mac, two iPhones and and iPad in the last few days and never turned off the firewall on my router. Something else has to be causing the lack of internet connection.

Same here, I update IOS devices at work each day, and recently my iPhone 5 to 9.01 then 9.02, never had to disable the routers firewall. I also never needed to disable the firewall for updating my earlier iPhones. Whatever your problem is its not your firewall causing the problem if its settings are the default. If you've customised the firewall settings you would need to look into whatever you changed.

By default the firewall is off on your Mac so disabling the router firewall, which is the prime protection, is unwise if left pernamently like that.

OK. I listen to you. I activated the modem firewall again. The macs individual firewalls are still "off". After a quick check on shields up on GRC.com, three ports were open (including 23 Telnet and 80 http) on the mac and all others were closed but visible and responding. Now all are in stealth mode. I will need to check again when the time comes for next iTunes update why I believe it blocked my connection between iTunes and the Apple servers. Service was very low yesterday. This may be the reason. Thank you all.

If you got the error I think you did that can occur even with a high-speed connection. I got it recently on a day when the Apple servers appear to be swamped with update requests. A slow speed connection will produce it consistently but even with a high-speed connection the error can occur consistently if the servers are swamped.