I alternate hoods and tops on flats, and when I feel like stretching or in a strong headwind, I use the drops (in the deepest part near the brakes if I'm riding near anyone/anything, and once in a while in the flat section of the drops where I can't touch the brakes).

Only hoods uphill. Especially when standing.

Downhill: I suggest never using the hoods on a fast downhill. Only the drops. I have heard a story of hoods coming off the handlebars and it sounds plausible, although rare, to me. So I keep as little weight on them as possible, which would be hard when going downhill. With a little practice (which you can get on the flats), you'll get better steering power and certainly much more braking power and finesse when in the deepest position of the drops (with access to the brakes).

Practice is everything...