No I haven't yet called my ISP, simply because I have a feeling they will simply tell me that they do not offer support for the modem and that I should instead be in contact with Zyxel's customer support.
If everything else fails, I'll still give it a go though.
It does indeed seem like the issue is the modem. At your suggestion I fiddled with it a bit...
The wireless has three security settings; No security, basic, and more security. The last is obviously recommended and what I've been using. When I turned it to Basic, it said WPS is enabled and thus I can only use More or No security.
No idea what WPS is but fair enough and turned it to No Security. Nothing meaningful change, until, on a whim, I left it on No Security and rebooted the modem by physically turning the power off. I left it like that for ~10 seconds and turned it back on, and voila, suddenly my iphone could browse the internet. I also tested some apps, like the Simcity game and they worked flawlessly.
I then changed the setting again to More Security and changed the password. Again, same problem; my iphone could connect to the Wifi just fine but again could not browse. I turned the model off and on again, and voila, worked. I changed the password again and had to repeat the on / off routine for it work.
Seems there is something about it that requires the modem to turn off and on before it will work properly again.
Any idea what that could be?
On another note, seems my lap top with linux mint 17.1 can no longer detect my wi fi network. I noticed it on the first reboot. It did show up for a very short period on the second reboot but now it is gone again. It can detect a lot of wi fi networks in the area, including my neighbor's but, for reason, again cannot detect my own, home wi fi.
Seems really bizarre. Got any ideas for that?