Motor for a winch (with controller and external power supply)
Is it possible to arrange my 12V stepper motors to exert 50 Newton of tension, using the 5V supply from MEGA?


No, you should never ever power a motor through an Arduino. It can only provide a limited amount of current, before it gets fried. You need to provide the motor driver with voltage directly from your power source. You haven't stated, what you are using as a power supply. I assume, you are just using an USB port of a PC. That is also a no-go, since it will only provide 500mA at max (that's even less, than the Arduino can bear). You should power your motor with a power supply of 12V, since it is rated for that voltage. You can buy a simple wallwart for that.

Also, currently you are providing the 12V motor with only 5V, so it cannot give you it's full power. Use a power supply with the correct voltage and more than enough current capability. Though you should keep an eye on the current ratings of the ULN2003. The datasheet is not really clear, if that chip supports 12V supply voltage. Some variants like the ULN2004 seem to support it, but I'm not sure about the ULN2003. If it is not rated for 12V, you can destroy the chip that way.

We cannot know, if the motor with it's driver will be able to rotate the winch, since the seller does not name the torque of the motor. You could try to contact the seller and ask directly about this. More specialized sites, where you can buy motors, will tell you exactly, what the torque of the motor is, that you are buying. Buying a cheap part at Amazon is somewhat the lightweight variant of buying it directly from china: The documentation is a bit better, but still not great. Without documentation or information from the seller, you are stuck with just buying and trying.


  is there a shield for my MEGA which can enable these motors to
  function in parallel?


It isn't clear, what you mean by that. You can control as many motors simultaneously, as you have pins and as you have enough computation time (meaning not too much steps per second or other stuff going on in the program). As mentioned above the power has to be supplied to the drivers from outside of the Arduino, so that does not apply here.


  otherwise, is there a strong continuous servo with an external power supply that would work here?


Power supply and motors are 2 different parts, that aren't usually sold together. Also you should start with the motor: Look for a motor, that can provide the torque, that you need. Then look for a driver circuit, that can provide the functionality, is rated for the same voltage as the motor and can provide enough current for the motor (the max. motor current is also information, that a good seller will provide). Then look for a fitting power supply. Unless you are buying some kind of kit, you need to choose these parts yourself. (We don't do product recommendations here)



A possibility, that you might not have though about: You could buy a normal DC motor, which provides enough torque. As speed is not your biggest concern, you could buy a geared DC motor, which can be rather strong. For a driver you would need to buy or build a H-bridge controller (which is essentially just 4 transistors put together). Be sure to use a MOSFET based driver, if you want to buy a driver chip. The standard L298n is pretty lossy.



It seems, that you generally don't know, how to build such a project. So here are some notes, that might help you with that:


Connecting everything together: In most cases (and especially when handling high current motors) you cannot get around soldering. You can buy a perfboard (cheap PCB material, with some pads already connected for ease of use), put the parts onto it and solder everything to the perfboard. Using shields as no-solder solution can only work, when you find a fitting shield and fitting motor for your requirements. That can be a far fetch. So if you want to get into electronics and Arduino, you probably should get yourself a soldering iron (there are also many tutorials about using it on the web).
Connecting the power supply: When buying a walwart power supply, it will normally come with a cable attached to it. At the end of this cable may be a connector. You have 2 options: Cut the connector and solder the wires in the cable directly to your perfboard, or buy the counter part of the connector, which you then can solder to your perfboard. Depends on if you want to disconnect the power supply from the circuit or not.


As I'm suggesting here to invest in this a bit, I want to also sketch an alternative, if you just want to get it work and don't experiment (this site is full of makers, you do this for fun, but that does not have to apply to everyone):

You may be able to use a shield to do, what you want to. This might cost a more, than putting the parts together yourself, but it will safe you the investment in tools, which you might not need in future. As above you need to choose the parts fitting your requirements. Decide on the type of motors, that you want to use (if money is not such a deal, you can nearly use any motor with enough power, stepper motor, DC motor, ...). Look for a shield, that can provide the needed current and voltage to the motor.

Every motor shield has a terminal for connecting the external power supply for the motors. On good shields this is a screw terminal, so you would simply strip the cable of the power supply and put the wires of it into the screw terminal.