There are a number of factors that might affect the answers but:
-Where can I eat?
There are places like McDonalds, Pizza Hut, Starbucks etc very close to GMex, and basically anything else you'd expect to find in a city within 10mins walk.
-Where can I park?
GMex has a car park. There are other car parks in and around the Great Bridgewater Street. Failing that, there are free carparks along the Metrolink tram route - you could park in one of those and then travel in by tram
-Where can I put my luggage on the first day?
Can't really help with this. I'd assume that there is somewhere in GMex itself.