Maybe none at all. Wearing a cross seems to be a trendy thing for young people these days. It might vary from diocese to diocese, but in my family, wearing a cross was seen as a Catholic thing to do, not something Anglicans did.
Well, could be. But from what I recall, Kate wears a very simple, unobtrusive cross - kind of the thing someone gets on their confirmation. The trendy crosses these days tend to be more ostentatious. I have a funky pink one I wear from time to time, and I have an Irish celtic necklace that looks like a rosary. They're trendy. Again, it's the simplicity of the piece that suggests she's religious. I find it odd that someone in her position would wear such important symbolism during a royal duty if she were not sending a signal to the world of her religious sentiment.
Again, I don't mind if she's religious or an atheist going through the motions. I am trying to look at her as objectively as possible.
Personally, I think that separation of monarch from church will be a difficult think for Britain, and commonwealth nations. Nobody believes in Divine Right, but still, the separation is part of a slippery slope towards the ordinary. For monarchy to survive, the must maintain the illusion of extraordinary. They are ordinary people, but they must live extraordinary lives.
The British royal family to me has always embodied stability and tradition. I think it's tradition in Britain, as it is in many places, to get upon on Sunday and go off to church in your spiffy clothing. There's many a non-believer who does it, believe it or not, recognizing that tradition, continuity and comfort that comes with attending church and a sense of belonging, a sense of national unity.
Even if the majority of Brits sleep in on Sunday, I think they still want to see the Queen (or the King) get up and go to church. The monarch sets the example. The example here is the importance of family life, tradition and all of the niceties that make up a routine.