CARBON FIBER HOOD

Do you need to use stiffening strips when fabricating a carbon fiber hood?

Yes. If your talking about the mold. The part I think would be strong enough. But the mold has to carry the weight of both the part and mold and any bow or twist wile curing will be permanent in the new part.

what he said ^^^

If it is to be secured on the car around the perimeter with dzus style fasteners, then no. If you plan on a hinged set up, then yes.
The mold is where you need to spend all your time. As stated, any deficiencies in the mold will be permanently transferred into all of the finished parts that come out of it.
One good mold is valuable, so keep that in mind. Make the buck very rigid.

Not enough info to give a precise answer.
Remember CF is rather stiff itself, the chosen grade of epoxy also adds a bit of stiffness, but at the sake of brittleness. In a large relatively flat surface you have 4? options:
1. Increase the thickness of the cf, adds weight/cost
2. Add thickness to only selected needed areas, see #1 to lesser degree
3. Add ribs in needed locations, big increase in stiffness but requires space for proper rib location
4. Add depth to majority of the item by using an internal lightweight filler, as a sandwich, with honeycomb/divinycell/foam/mat, the last being the heaviest solution.