DE comes in 2 forms. One is sold for pools - this has added checmicals in it you do NOT want to put anywhere near cats or a garden, the chemicals are no good for anything but pool cleaning. The second is in powder form you can purchase at most garden supply stores. Check the label and be sure DE is the ONLY ingredient.
Yes you can let the cats eat it, you can sprinkle some of the powder on their food to help combat intenstinal parasites. I would not use too much since the cats might reject it. A tablespoon every week should be enough.
You can not spray it. Adding water to DE will disolve it making it pretty much non functional, after rains you must reapply it it where it was previously applied.
Putting it down where the cats are sleeping is a great idea because it will kill emerging fleas. You can also place it around your house and in your yard however it is an indiscriminate killer and will kill other insects.
When applying use a mask to avoid inhalation and dont apply when too windy or wet, reapply after rains.
It would be so much better if you could use frontline or advantage, but im not sure how you could apply it monthly. Good luck