Others with more expertise can chime in, and I hope they will, but what you describe in #1 sounds precisely like the drawcord having been disconnected from the carriage (or maybe it's broken). It hooks on to the right side of the carriage, underneath, and is connected on the left side to the drum (the small wheel you mentioned) which encloses the typewriter's mainspring. The cord pulls the carriage to the left (i.e. allows the carriage to advance all the way over to the right side of the paper).

The cord needs to be reattached to the carriage. You should find a hook or maybe a screw projecting from the underside of the carriage on the right side. You also need to turn the drum a few turns (3-4) to wind tension on the spring -- that is what gives the motive power to pull the carriage all the way over to the left.

I think you said the cord is attached to the drum? Can you unhook it from the drum? I ask because it's probably easier to disconnect the cord from the drum and instead attach it to the end of the carriage, and then use something like a bent piece of shirt hanger or a long wooden skewer to thread the cord back underneath the carriage to the drum. Once you've done that, wind up the drum as mentioned above, and hook the cord back onto the drum where it's currently attached. You may need to tie a knot on both ends of the cord to ensure you have a firm loop you can hook over the attachment points on the carriage and the drum.

I don't have one of these typewriters, so I am speaking only in general terms, but this is a typical setup for typewriters (and a common problem). Search around here and on the internet for "drawband replacement" or the like. Maybe others here can point you to a link on this forum, and maybe others are familiar with exactly what to do with this typewriter model.

Thanks Fleetwing! Your advice helped, as I discovered the drawcord was basically destroyed after it fell off the drum and was caught in the gears of the carriage. I replaced the drawcord with strong fishing line and have attempted to properly reattach it to the drum. However, when I attempted to set the tension on the drum to re-attach the drawcord, there seems to be an issue with the spring thats inside the drum. 

I wind the drum several times, attach the drawcord, I begin to hit keys and the carriage moves as it should. Then, about 2/3 the way, the carriage stops. I watched what happened from below as I push the spacebar. and basically the tension on the drum is lost and the drawcord goes loose on the drum. I attempted multiple ways to adjust more tension to the spring and start over again, but every time, it seems that the tension inside the spring makes a click/grinding sound and the tension drops.

Does anyone have any idea why this is happing or how I can fix this? Advice is greatly appreciated!

Ok, will do! Thank you for your response!