"Also, does a particle move fastest where the potential is lowest/magnitude of strength of electric field is highest? If yes, then why?"
It moves fastest when it has the most ke, when there is the greatest potential energy decrease, so, in this question, when the potential is lowest.
At that point the gradient of the potential is zero, so the electric field is zero.
Remember electric field strength tells you force, when force is zero that means acceleration is zero. In this case it's been getting faster, so a=0 means it's now at max speed, as it moves further the force changes direction and the acceleration becomes negative, the particle slows down till it reaches sphere B.
I hope that helps your understanding.