I recently serviced one of these motors for the first time, so here are some pointers from someone not much more experienced than you:
First, see if you can get between the reduction gear and the motor frame with some tweezers... you might be able to lever the stud back out of whatever hole it has fallen into. Then glue it in place.
If you have to get inside the motor, you should get a wheel-puller. A wheel-puller is one of those things you will find reasons to use if you have one, so I would get something good. Portline has one for $50 here: http://www.portlines.com/tools2.htm. Or you can go cheap and get one that's made from a battery terminal puller (look on ebay).
These motors are famously hard to put together, but the service manual pages give detailed instructions. What I did, when taking the motor apart for the first time, was to follow the assembly instructions in reverse. Each time I removed a part, I immediately practiced putting it back in again, to make sure I understood how it fit, and that I could still close the shell up after installing it. This was especially important with the pawl assembly. Doing this saved me all kinds of frustration later, and I got the motor back together successfully on the first try.
No need for wheel cups. Tolerances are so loose on these motors to begin with that using special wheel cups for this motor truly is putting lipstick on a pig. ... When you go to put the wheels back on, just use a vice with jaws that are reasonably square to each other. There is no rod connecting the front and rear drivers, so you don't have to worry about quartering.
You will probably not be able to get 100% reliable reverse unit operation, so don't pull your hair out trying. Your friend probably just wants it to work, not to be perfect.
These are just not great motors. Lionel was trying to make a price point, and they were never going to put the time and money into finishing each part to the point that it operated flawlessly. To make matters more frustrating, it's difficult to troubleshoot since the black plastic shell prevents you from seeing what is going on inside. Yet, some extremely clever engineering went into these things, and I have nothing but respect for whoever thought this motor up and made it work. Personally, I enjoyed tinkering with it and learning what makes it tick.