What is the difference between Dual core, Core-i3, i5, i7, FX, Fusion and so on? which one to buy ?

Every CPU has n number of Cores. Minimum being One Core. Dual Core has Two. Likewise we can check how many cores that CPU, we are interested in, have.

As a rule of Thumb, More number of Cores, better the performance. More Desirable - If Pocket Allows :-)