I'm curious why you see this as the most important issue for you. Say you did open up: there'd be nothing to stop someone opening up the day after you, so even if it did check out 100%, you'd be no better off.
The obvious things to check would be the managers of the shopping centre: just ask them. Also, any recent "change of use" planning applications.
My advice would be to put together a comprehenive business plan: competition will certainly be included in this, but it's far from the most important thing to consider.
By the way, do you have any experience in the cafe or other food business?