1) Don't worry about the solenoid - just replace it. They are a common failure anyway. Standard (SMS) SS581. Suggest you drill out the rivets and look inside for how they work. You can often revive them by taking them apart and burnishing the contacts / flipping the disk over. Take it apart, examine, throw in trash.
My point was that 5 ohms translates to 2.4 amps at 12V, and 29 watts heating. Seems pretty reasonable for a solenoid coil that's used intermittently.
2) Dunno about the carb wires. My limited understanding - the carb "ECU" runs the stepper motor on the idle jet that makes the 258 somehow emission compliant in this era. You can bypass the whole thing following a procedure termed "the Nutter bypass," which was worked out by a well-known Jeeper John Nutter. Most of the info re the bypass will be in the CJ/YJ forums, not in the FSJ forums. There are many more of these CJ/YJ Jeeps out there than like your Jeep.
I'd pretty much have to trace it out from what's online, the TSM description, and the wiring diagram. Also, it would help to have the Jeep in front of me. I don't think there's any alternative but to sit down with the sources and figure it out, on paper if needed.
3) Regarding the butt splices, you'll just have to pry them open with whatever you have on hand. Small pliers, screwdrivers, ice pick, whatever. Pretty sure Jeep does not solder these, but they would have used a high-quality crimping tool that closes the splices much tighter than you can do by hand, at least with the crimping pliers shadetree's typically have.
The splices are uninsulated butt (aka barrel) connectors. In the past I have sourced them from Mouser Electronics, but my latest source has been Del City
https://www.delcity.net/store/Non!Insul ... 0.h_801871
I put some discussion here -
http://www.earlycj5.com/xf_cj5/index.ph ... st-1571304 - though you may need to join EarlyCJ5.com to see the embedded pictures.
JMO - I'd abandon the nichrome wire and get the ballast resistor noted above. That way you can completely rewire this part of the harness with all-new wire and connectors. The ballast resistor is a factory part for a '70s Dodge - I sold plenty of them back in the day. Typically what you'd get if you asked for a generic ballast resistor. Nothing wrong with using the separate resistor - the resistance wire probably lowers production cost and speeds assembly on the line. Or maybe somebody has the complete wire for you from a wreck or part-out.
Putting a splice in the middle of the resistance wires raises some problems. First, you need a small enough butt connector so that it fits tightly on the small-gauge single strand wire. You need a lot of pressure to get a good crimp on this hard, single-strand wire, and it might come apart in service. Plus with the connector on there, you can't slip the tubing over the whole length. Heat shrink would be ok. I strongly recommend 3M adhesive lined heat shrink for these application. Available online lots of places, including Mouser and Parts Express.