What are the consequences of connecting two motors in parallel?
A simple PWM controller will cause each of two similar motors connected in parallel to run at approximately the same speed (with some minor change on each due to loading). That is because the resistance of the rotor winding is small, back EMF is proportional to speed and torque is proportional to applied voltage minus back-EMF (divided by rotor winding resistance). To a first approximation, speed is proportional to applied voltage, and a PWM source behaves like a constant voltage (not like a series resistance).

However, a more sophisticated controller with IR compensation or back EMF measurement will cause the motors to interact and loading up one motor more will cause the other motor to increase in speed, while not providing optimal control for the first motor. A closed-loop controller with feedback of some kind (tacho) will act similarly- the motor with feedback will be controlled well but the other will speed up and slow down in sympathy with the loading on the controlled motor.  

It really depends on the nature of your motor controller. 

In answer to your specific questions: 


If one motor stalls the current will increase. If the motor controller can supply the full stall current plus operating current for the other motor then the non-stalled motor will be unaffected. Otherwise, it will slow down or may stall. 
All DC motors produce back EMF- it's proportional to the rotational speed. 
No, since it's proportional to rotational speed, at speed = 0, back EMF = 0. There's going to be inductive 'kick' at 0 RPM which is unrelated to motor RPM, but related to motor inductance (and current, which is high- perhaps even high-est when the motor is stalled).  
You should follow the protection and fusing recommendations of the motor controller and the motor manufacturer and seek help if there is a conflict between the two.