Yes, it's fine on my PC. However, many lower-end mobiles like this one don't support full CSS2.1 specs, and I'm pretty sure that includes position: fixed.
I will if I can work out how. I don't think there's a built-in feature, so I may end up having to take photos of the phone. Won't be until tomorrow, though.
It's a Vodafone own-brand, but it uses Opera Mini, which is a very common mobile browser. Mine is version 5. There is a simulator running version 6.5, but when I tried your site on it, it doesn't work quite as well as it does on my phone.