i am getting black soot on the back of my car on the trunk from the exhaust

Black suit out the exhaust has to be a sign of burning oil. Is the engine consuming oil between oil changes? A cylinder leakage test may be worth while to see how much blow bye the engine has past the rings. If the engine or turbo are causing oil to enter the exhaust the life of the catalytic converter will be shortened.

The Mazda Speed3 run on the rich side, if your heavy footed and do a lot of city driving it may be normal. Its more noticable on lighter color vehicles. I would still recommend for your peace of mind having the dealer check the vehicle out just to make sure. The powertrain warranty on your vehicle should be 5yr/60k on engine and turbo.