They'd probably need to use old or even demonstration tyres, seeing as otherwise Mercedes would have an advantage (or so other teams would complain). A 2011 car might even be easier for him to get into than a 2013 FRIC, DDRS, Coanda exhaust Mercedes though, more akin to his old Renault.
And with older tyres presumably? Not that either of these (2011 car & old tyres), would have a massive impact on his reasons for testing. If he can fit in the cockpit and drive the car at speed then it will be a good indication.
Where would they test? Silverstone?
As for location, they're free to pick any FIA approved test track. Silverstone is next door to the Merc factory, but also has the disadvantage of unpredictable weather and a lack of privacy.