Question

Since exothermic reactions give off heat, they are exceptions to the law of conservation of energy and they are able to create new energy.

Answer 1

They are not exceptions. They are changing energy which is stored in the form of chemical bonds into another form, notably thermal. This is also not related in anyway to the energy / mass relations expressed most notably, if tritely, by E=mc^2. But no, you cannot create or destroy energy. i hope i helped