What defines camera's size? Smartphone camera is small while others are big. I know some functions like zoom can change physical size and multi lens,.. etc
So, assume that a without zoom, what define camera lens?
I want to get the general idea why smartphone camera is very small? Its advantages and disadvantages
What is it limit? E.g if sensor'size could be shrunk, could camera size be shrunk?
 A: Mostly the size of the imaging chip (or film)
As the image gets physically smaller, the same field of view will be produced by a shorter lens. The image chip in a modern digital SLR is 1/2 to 2/3 the size of traditional 35mm film and so the lenses (and the camera) can be made smaller and lighter. Compact cameras have smaller sensors and phones smaller still.
There is a limit to making the image smaller if you want high resolution (a lot of pixels). As you make the pixels smaller they each receive less light and so give a noisier signal - especially in low light. Finally there is a limit when the pixels shrink to close to the size of the wavelength of light, say 1/1000 mm.
A: The size of the sensor is equally to number of pixels times the area of one pixel. So increasing the number of pixels clearly has an effect on the size, but so does the size of each pixel.
The smallest sensor pixel in conventional photography you can have will be limited by the diffraction limit of the lens that you use, which depending on the lens is usually somewhere around 0.5 to 1 micron. There is little point making the sensors smaller than this since it will not be able to resolve any changes.
The size of the sensor has two main effects on the final image captured. Smaller pixels capture fewer photons so the signal to noise ratio goes down. The ability to capture images in poor lighting is therefore degraded. The other effect is more artistic. Larger sensors have a narrower depth of field, meaning objects can go out of focus. 
These two effects make it desirable to have larger sensors. To ensure a reasonable image quality the larger sensor is going to require a larger lens to cover its area. (Larger lenses also have more light gathering capabilities and so potentially produce better images.) 
In summary, the larger the camera, the easier its to make higher quality images, but this has to balanced by the desire to have a small compact camera that fits inside a phone for example. 
A: "What is it limit? E.g if sensor'size could be shrunk, could camera size be shrunk?"
Even if sensor sizes could be shrunk without limit, the camera size would still be determined by the diameter (aperture) of the lens. And the fundamental point to note is that the wave nature of light makes it impossible to reach an angular resolution $\delta \phi$ (in radians) unless one uses a lens with aperture $D$ satisfying the Rayleigh criterion:
$$D > 1.22 \frac{\lambda}{\delta \phi}$$
Here $\lambda$ represents the wavelength of the light. 
To reach the angular resolution of a human eye with nominal performance ($\delta \phi \approx 0.003$ radians) for green light ($\lambda \approx 0.5 \times 10^{-6}$ m), it follows that the required aperture $D \approx 2$ mm.
One can utilize smaller aperture camera objectives, but no matter how much effort is put in optimizing the optics, one would never reach the resolution of the human eye.
