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I have tried all suggestions in comment but no good result. Finally, I added a 100 µF capacitor to VCC and GND of Arduino (5 V), and remove the 1 kΩ in pin 11.

Here's the update:

and the code:

  void setup()   
  {   
  Serial.begin(9600);   
   pinMode(11,OUTPUT);  
   digitalWrite(11,LOW); // Normally LOW inthis pin   
   pinMode(A0,INPUT);  // 10k Potentiometer   
  }   
  void loop()   
  {   
  int s=analogRead(A0); // 10k Potentiometer   
  int z=map(s,0,1024,0,255);   
  Serial.println(z);   
  analogWrite(11,z);   
  } 

Temp Result:

1. The motor is not too hot anymore.
2. I still have motor vibrations.
3. Motor speed cannot reach the max speed (I'm sure this is because of the vibration)

UPDATE 2

1. I change the thick of the wire. I use all the same wires. Result = No heat.
2. I remove the 10Ω and the speed can reach the MAX Throttle/speed. Yeah! (based on this article).

By doing the two above, I finally didn't see the vibration!!!