Does the Dime model say anywhere that it is a Dime model? I can't really tell from the small photo, but it looks like it could be the regular ML model, which is the design that the Dime guitars are based on, but a bit cheaper. Either way, it's probably got a tune-o-matic bridge, and I suspect it's probably legit.

As for the Hammett, "materials" do sometimes make a difference. I haven't played any Hammetts, so I can't make comparisons between sound, but these are the basic differences:
-- LTD KH-202 ($400-$500): bolt-on neck, basswood body, ESP pickups, licensed Floyd, flat neck contour
-- LTD KH-602 ($1100): Neck through body, alder body, EMG pickups, original Floyd, U-shaped neck contour
-- ESP KH-2 ($2100): Adds Gotoh tuners instead of ESP tuners. Honestly doesn't look much different from the $1100 model to me, with the exception of the tuners (which shouldn't add that much), the ESP logo and the Hammett signature on the headstock. They say it's "the exact guitar made to Kirk Hammett's specifications," but I don't really see any difference in components from the model that's $1,000 cheaper. Could be made from better grades of wood, i suppose, or you could be paying a grand for the logo and the signature. Maybe someone else knows?

I don't know of a Hammett model with a 3+3 tuner set up, but a lot of the LTD models have 3+3 setups.