As I know, due to Coriolis force, hurricane in each hemisphere can spin in one direction only. But I also know hurricane can be formed near equator, which colriolis force is weak. My question is, is it possible that a vortex spinned in opposite direction is developed into hurricane near equator?
No, a small vortex in a contrary rotation might develop into something larger if conditions were right, and there was no horizontal shear, but it wouldn't last long. The Coriolis force would work against it, and it would fizzle out.
Also, hurricanes don't form near the equator - there isn't enough horizontal rotation to kick-start it. Hurricanes initiate a little to the north or south of the equator.