If you add it to the cat food, make sure it is food grade. And it is hazzardous to inhale.
Yes, it is used as a "natural" treatment for bugs, especially fleas.
The idea behind feeding it to pets is the sharp edges of the pieces of DE are supposed to kill worms.
While a cough can be a sign of worms, it is usually a severe infestation at that point. DE is not going to work quickly enough to help your cat. The cough can be a sign of many things and a vet should be consulted for treatment. You don't want to be treating for worms when it is really a heart issue, for example.
Skin kids - Jason, Kevin, Allison
Canine kids - Bennett & Bailey (always in our hearts), Riley, Banker, Rogue and Boz
Feline kids - Zoey, Talley and Abra