What I have since learned: (Tell me If I am wrong)
In circuits ,Batteries provide electric potential difference (voltage) ,This difference creates electric field (Over the conductor or the wire) which applies force on electrons ,This makes an flow of electrons through wires which called current.
In another way ,We can say batteries provide electrons with potential energy and this energy converts to kinetic energy and flow in the circuit ,So potential energy is used up.
I have learned also that electric potential of an electron depends on its position in electric field.
$Q$1: Since point $a$ and point $b$ are in different positions in electric field (produced by voltage of the battery) Why have they the same electric potential , Why is there no voltage drop?
$Q$2: As I have mentioned ,Potential energy of the electron converts to kinetic energy ,Now when electrons flow through a resistor ,why is there a voltage drop?
On $Q$2: I say there isn't voltage drop because when electron flow in the resistor ,Some collisions occur in the resistor ,So electrons lose some of their kinetic energy ,But due to the electric field ,Electrons accelerate again and restore their lost kinetic energy ,So why is there a drop in electric potential or voltage drop?
$Q$3: My last question about drift speed. Because electrons are in electric field ,Electric filed applies force on them ,So they accelerate ($F=ma$) ,So their drift speed $Vd$ must be higher ,hence the current $I$ must also must be higher ($I=NeVdAQe$).
Please ,I am so confused and I can't understand this.