and I never let to run those 60mA for more than 2-3 seconds.
Doesn't matter about how long you are damaging your arduino pin.
m, I've read about 40
40mA is a stress rating not an operational rating, do you understand the difference? If not read the processor's data sheet, the section on electrical characteristic. You will damage your arduino if you run at 40mA or above.
200-220mA without load. With load.. 1700mA.
So that is why your transistor is getting hot. Yes it is normal for a motor to draw more current when it is under load. The ultimate load is a load that is enough to stop the motor, then it draws what is known as the stall current.