What is the speed of the conversion of light to electrons in a photoelectric cell? How small can they make them? Why don’t they use it in processors where light completes circuits? 
PerfectDark
I’m not an expert, or even a well-informed amateur, in this field but I do know there is a lot of current research on optical computing. The answer to your question is, roughly, very fast.
Think about fiber optic cables – they have very high bandwidth, very high frequency operation. At the end of the FO cable there is a converter to convert the signal back to electrons – it’s got to be faster than the highest frequency signal.
Physically, a photodetector is based on photons knocking electrons out of orbits – a very high speed event. Presumably the fastest detectors can detect very small numbers of electrons and would themselves be very small. Like electronic devices, if my reasoning is correct, the faster they are the smaller they have to be.
Any more knowledgeable people out there who can quantify these answers?
“What is the speed of the conversion of light to electrons in a photoelectric cell?”
There is no time lag between the absorption of a photon and the emission of an electron. Absorption occurs in about the time it takes a photon to traverse a molecules electron cloud [Somewhere ~ 10E-14 sec].
“How small can they make them?”
Photocells could probably be made as small as transistors (10-100 nanometers) without too much effort.
“Why don’t they use it in processors where light completes circuits?”
There aren’t many such devices made yet. What with the inefficiency of converting light to photons and back as well as the absence of methods to make arrays of light based logic gates etc. it’s not clear that there ever will be.
Light based computers are right up there with molecular scale computers in terms of current feasibility. There are a lot of interesting possibilities, but also many problems that could make such devices impractical for years to come.