What's wrong with my replacement fan motor?
An electric motor in definitely not not just an electric motor.  They are very proprietary. It takes a lot of skill substitute one motor for anything but the OEM part number. There are tens of thousands of different kinds of motors out there.  Almost none of them will substitute one for another.  For example, with the motor you are working with, the stack of the iron laminations determines the torque the motor can deliver.  The torque required is dictated by the size the design of the fan blade; the larger the blade the more torque required.  I can clearly see that the motor you are trying to substitute will not provide the necessary torque to drive that blade, i.e. the original motor stack is so much thicker.  This is just one of many variable that are in play.  If you can clear the following list of variables you may be able to replace this motor successfully.  #1 support/mounting criterion.  #2 direction of rotation.  #3 Torque.  #4 RPM. #5 Shaft length. #6 shaft diameter.  #7 Shaft configuration. #8 clearances.  #9 Voltage requirements. #10 What environment was the motor designed to operate within.  

Answer to question #2:If the motor still runs nicely it probably OK.  These motors die because the bearing dry out. The lubrication last only lasts so long.    

Answer to question #3.  If you are getting proper voltage to the motor and the shaft doesn't turn the bearing are probably shot. With the lubrication gone you have metal on metal and it's only a mater of time.