What wire size for 100 Amp sub panel 100ft in length form 200 Amp main panel?
Alright here we go. A circuit size is defined by the overcurrent protection not the of the equipment attached to it. For example your question. Are you planning to protect the circuit with a 100A breaker? If the answer is yes then you need to run at least #3 Copper or a #1 Aluminum conductors. If you install a 70A breaker then you can reduce your conductors to #4 cu or #3 al. Of course none of this takes voltage drop into consideration.

Voltage drop is calculated using your power demand or all of the electrical equipment, lights, devices, and appliances you are planning to use at one time. If you don't have that information then would it be safe to assume that you are using the 80% rule on your feeder size? Meaning you are only going to load your circuit to 80% under normal circumstances. If the answer is no I want to use the full 100A then you feeder would have to be raised 2 sizes to make up for the voltage drop to a #1 cu or 1/0 al. If the answer is yes then you will be able to stay at the original size. The main reason for you to consider this is the cost of material. Conductors a few size larger can become rather expensive. Which is why I mentioned a 70A feeder which would also reduce your cost. I would suggest you take a good look on how much power you are going to use and think about what size feeder you are going to need. 

As far as whether you can reduce a neutral once again we have no knowledge as to what type of equipment you are using. If all of the load is 120V then no. If there are some 240V loads then yes but we have to know how much will be permanent.

Your grounding conductor must be run also and it is sized to the breaker also. A 100A breaker would require a #8 cu or a #6 al. If you are calculating full load then the grounding conductor must take voltage drop into account and rise a full two sizes more just like the current carrying conductors or a #4 cu or #2 al.

So once again take some time and think about what you need. I hope this helps or at least sheds some light on what you are trying to do. Good luck.