Harman ST-5 Turntable RabcoTonearm and Cart

Very new here so sorry for a somewhat basic question.  I did some google searches (found the manual for the HK ST-5) and searched this forum but did not find exactly what I am looking for.

I just picked up an ST-5 and knew it was going to need some work.  The cartridge is an Ortofon LM 10 but it looks like it is broken.  It is just a rectangular tube with "LM 10" on it and a tapered metal extension without a stylus protruding from the front.  The "neck" which attaches to the tonearm is not there and the red wire seems to have broken off from the clip.  I thought I could detach the tonearm to have a better look because in the manual it looked like I could do that.  I unscrewed the knurled nob where it meets the main assembly and I thought I could just pull the tone arm off the socket.  Instead, the aluminum tube came out but what looks like a sheathed wire stayed attached to the base of the tonearm assembly.  So my questions are:

1. Should I be able to detach the tonearm?  Can I just gently work the sheathed wire off of the main assembly on the turntable?
2. Now that I take a closer look, it seems only the green wire is still attached to what remains of the cartridge.  Is it easy to just strip off some insulation from the broken wires and resolder the clip or is it better to try to replace the entire wire assembly? (If easier to replace, can anyone suggest some sources?)
3. Is the cartridge itself broken or is the "neck" and stylus just additional pieces that are easy to purchase?

Thanks for any help and info.  I don't dabble that much with vintage equipment (or any equipment all that much, my current turntable is a Technics SLD2) and this was a bit of an impulse buy for me.  

OK, I got brave enough to carefully pull on the exposed tonearm wire where it connects to the carriage assembly.  As you might have thought, the issue was the black plastic DIN piece came out of the tonearm itself instead of unplugging from the carriage.  

After examining the cartridge up close, it's apparent that it cracked off of the tonearm.  I can only surmise that someone tried to replace the stylus at some point and ended up breaking the cartridge and pulling out some of the wires.  Hopefully an easy fix??

Easy? That would be too easy. But from your description, not terribly difficult.
As I recall that arm used a cartridge similar to a P-mount. The cartridge was probably sheared off in an accident and the 'table left for dead.  Is the connector still intact?
The wire coming out of the tone arm has four pins that connect directly to the back of the cartridge.  Unfortunately, only one of the four is still intact.  I think I have enough slack to carefully cut away the insulation and resolder the pins back on to each wire.  If you have any ideas or tips as to whether this is a good idea or not please let me know. (eg - do I have to use a special solder or is standard OK, should I sheath the wire in shrink wrap or not, etc. etc.)

Since I started this post, I've done some more research and ordered a new Ortofon OM10 (which arrived safe) and a stylus alignment tool from Shapeways that someone on this forum was kind enough to re-create.
I also pulled down the user guide and technical manual from vinylengine.

Also in my research I've happened upon countless tales of how hard it is to tweak these linear tracking turntables so that it tracks perfectly straight across the record.  I guess I'll have to take it one step at a time to see how badly this unit has been maintained.  Judging by the amount of dust on it (since it didn't have a dust cover) I am guessing it's been sitting around in this condition for a while.