If we use Cryengine 3 for game development and make the game 3D compatible. Because 3D sends out two pictures, will this mean that you need a computer with twice the "power"? So if you get 30 fps when playing normal you will need 60 fps for playing with 3D?
In short, yes you will need to be outputting 60fps to have the effect of 30fps.
You do not lose half your performance when turning on stereo 3d. The games logic, AI, physics, and anything the CPU does still is only run once. Only the rendering is done twice, and that is efficient, because the card has everything in memory for what each second frame is going to be, so it doesn't use any additional bandwidth.
The only situation where this will be true is if you had a static 3d scene that was really complicated with the GPU doing everything and the CPU sitting idle. And even then I doubt it will be a 50% drop in performance
I have tested a lot of games with nvidia 3d stereo, and no game ever dropped near 50% performance.
Especially with CryEngine 3 this is not true. Yes, it halves the framerate, but turning on 3D does not cost you half your frames (or you need doubled hardware power). They use a reprojection cache and the available depth buffer to get the second image, thus the performance drop is 5-10% when turning on 3D. They call this "Screen Space Re-Projection Stereo".
I would say not negligible at all. It's both a hardware resource problem and a development challenge.
Most of the time you cannot split the framerate between the two eyes; if your game usually runs at 60fps, you need to run at 120fps for the same visual comfort.
However, a lot of things can be done only once per stereo pair: frustum culling -- at the cost of a slightly larger frustum (see Setting up the 3D Cameras in Optimization for Making Stereoscopic 3D Games on PlayStation®), occlusion culling, vertex and index array uploads, scene captures and renders to texture...
Parts of the scene may be rendered only once: for instance, a complex sky with clouds, stars, etc. will usually be at infinity, so the pixel shader cost is only needed once, and the second rendering can be a mere texture lookup into the first render target. Actually some stereo games use a method called reprojection that builds on this approach to make it viable for the whole scene: see this thread at beyond3d for pointers to this technique.
To cope with the required extra processing power, you can reduce the resolution. From my personal experience, it is far more acceptable to do so than to reduce the framerate. Do not try to disable anti-aliasing, though: as Sony engineers say in the above paper, rendering to lower resolution buffers with AA looks better than high resolution buffers with no AA.
Note that there are other approaches to stereovision in games that don't need a 3D TV, such as Trioviz. I cannot go into the details here, though (NDA issues).